Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
928 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×(C22⋊D191)⋊C4 | C2 | semidirect |
| 3. C2×C22⋊C4×D191 | C2 | semidirect |
| 4. #27132551 | C2 | semidirect |
| 5. #27132543 | C2 | semidirect |
| 6. #27132539 | C2 | semidirect |
| 7. #27132534 | C2 | semidirect |
| 8. C4×(C2×D191)⋊C4 | C2 | semidirect |
| 9. #390×C191 | C2 | semidirect |
| 12. C23×Dic191 | C22 | semidirect |
| 15. #20259290 | C4 | semidirect |
| 17. C2×Dic191⋊C4 | C22 | semidirect |
| 20. C2×C22⋊Dic191 | C22 | semidirect |
| 25. C2×C4×Dic191 | C22 | semidirect |
| 26. C191⋊#95 | C22 | semidirect |
| 27. C191⋊#95 | C22 | semidirect |
| 28. C191⋊#95 | C22 | semidirect |
| 30. C2×C4⋊C4×C191 | C22 | semidirect |
| 32. C2×C22⋊C4×C191 | C22 | semidirect |
| 33. C2×C42×C191 | C22 | semidirect |
| 38. C23×D191 | C2×C4 | semidirect |
| 42. C2×C22⋊D191 | C2×C4 | semidirect |
| 57. C22⋊Dic191 | C2×C4 | semidirect |
| 59. (C2×D191)⋊C4 | C2×C4 | semidirect |
| 60. (C2×D191)⋊C4 | D4 | semidirect |
| 66. C2×D4×C191 | C2×C4 | semidirect |
| 142. C2×D191 | C4×D4 | semidirect |
| 157. C191 | #2358 | semidirect |
| 162. #390 | D191 | semidirect |
| 177. C2×C4⋊C4 | C2×D191 | semidirect |
| 186. C2×C22⋊C4 | C2×D191 | semidirect |
| 188. C2×C42 | C2×D191 | semidirect |
| 205. C2×D4 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259290 | 2 |
| C2×(C22⋊D191)⋊C4 | 2 |
| C2×C22⋊C4×D191 | 2 |
| #27132551 | 2 |
| #27132543 | 2 |
| #27132539 | 2 |
| #27132534 | 2 |
| C4×(C2×D191)⋊C4 | 2 |
| #390×C191 | 2 |
| #2358 | 191 |