Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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×#20259280 | C2 | semidirect |
| 3. #27132989 | C2 | semidirect |
| 4. #27132985 | C2 | semidirect |
| 5. #27132981 | C2 | semidirect |
| 6. #27132977 | C2 | semidirect |
| 7. #27132974 | C2 | semidirect |
| 8. #27132702 | C2 | semidirect |
| 9. #27132666 | C2 | semidirect |
| 10. #27132625 | C2 | semidirect |
| 11. #481×C191 | C2 | semidirect |
| 24. #20259280 | C22 | semidirect |
| 25. C2×C4⋊Dic191 | C22 | semidirect |
| 30. #20259256 | C22 | semidirect |
| 31. #20259255 | C22 | semidirect |
| 32. #20259253 | C22 | semidirect |
| 33. #20259244 | C22 | semidirect |
| 34. #20259243 | C22 | semidirect |
| 35. #20259242 | C22 | semidirect |
| 36. C22⋊(C191⋊C8) | C22 | semidirect |
| 37. (C2×D191)⋊C8 | C22 | semidirect |
| 39. C2×C4⋊C4×C191 | C22 | semidirect |
| 40. #106×C191 | C22 | semidirect |
| 41. #102×C191 | C22 | semidirect |
| 42. C22⋊C8×C191 | C22 | semidirect |
| 153. C191 | #3094 | semidirect |
| 160. #481 | D191 | semidirect |
| 182. C2×C4⋊C4 | C2×D191 | semidirect |
| 189. #106 | C2×D191 | semidirect |
| 193. #102 | C2×D191 | semidirect |
| 196. C22⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D191 | 2 |
| C2×#20259280 | 2 |
| #27132989 | 2 |
| #27132985 | 2 |
| #27132981 | 2 |
| #27132977 | 2 |
| #27132974 | 2 |
| #27132702 | 2 |
| #27132666 | 2 |
| #27132625 | 2 |
| #481×C191 | 2 |
| #3094 | 191 |