Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #27133138 | C2 | semidirect |
| 3. #27133137 | C2 | semidirect |
| 4. #27132772 | C2 | semidirect |
| 5. #27132743 | C2 | semidirect |
| 6. #27132699 | C2 | semidirect |
| 7. #27132669 | C2 | semidirect |
| 8. #27132621 | C2 | semidirect |
| 9. #418×C191 | C2 | semidirect |
| 11. C2×#15690272 | C4 | semidirect |
| 17. D4×Dic191 | C22 | semidirect |
| 18. #20259284 | C22 | semidirect |
| 23. #20259255 | C22 | semidirect |
| 24. #20259253 | C22 | semidirect |
| 25. #20259244 | C22 | semidirect |
| 26. #20259232 | C22 | semidirect |
| 27. C8×Dic191 | C22 | semidirect |
| 31. #102×C191 | C22 | semidirect |
| 35. C2×D764 | C2×C4 | semidirect |
| 39. #15690272 | C2×C4 | semidirect |
| 40. #15690272 | C2×C4 | semidirect |
| 41. C2×C191⋊C8 | C2×C4 | semidirect |
| 55. C2×D4×C191 | C2×C4 | semidirect |
| 108. C191 | #2948 | semidirect |
| 117. #418 | D191 | semidirect |
| 138. #102 | C2×D191 | semidirect |
| 149. C2×D4 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690272 | 2 |
| #27133138 | 2 |
| #27133137 | 2 |
| #27132772 | 2 |
| #27132743 | 2 |
| #27132699 | 2 |
| #27132669 | 2 |
| #27132621 | 2 |
| #418×C191 | 2 |
| #2948 | 191 |