Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#20259345 | C2 | semidirect |
| 2. C22×C8×D191 | C2 | semidirect |
| 3. #27133176 | C2 | semidirect |
| 4. #27132901 | C2 | semidirect |
| 5. #27132900 | C2 | semidirect |
| 6. #27132899 | C2 | semidirect |
| 7. #27132895 | C2 | semidirect |
| 8. #27132894 | C2 | semidirect |
| 9. #27132700 | C2 | semidirect |
| 10. #27132658 | C2 | semidirect |
| 11. #467×C191 | C2 | semidirect |
| 15. C2×#15690274 | C22 | semidirect |
| 16. C2×D1528 | C22 | semidirect |
| 31. #20259256 | C22 | semidirect |
| 32. #20259253 | C22 | semidirect |
| 33. #20259246 | C22 | semidirect |
| 34. #20259244 | C22 | semidirect |
| 35. #20259242 | C22 | semidirect |
| 36. C2×Q16×C191 | C22 | semidirect |
| 39. #107×C191 | C22 | semidirect |
| 40. #103×C191 | C22 | semidirect |
| 64. C8×D191 | D4 | semidirect |
| 118. C22×C191 | #135 | semidirect |
| 129. C2×D191 | #135 | semidirect |
| 145. C191 | #3050 | semidirect |
| 151. #467 | D191 | semidirect |
| 161. C2×Q16 | C2×D191 | semidirect |
| 181. #107 | C2×D191 | semidirect |
| 184. #103 | C2×D191 | semidirect |
| 274. C22 | #20259345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259345 | 2 |
| C22×C8×D191 | 2 |
| #27133176 | 2 |
| #27132901 | 2 |
| #27132900 | 2 |
| #27132899 | 2 |
| #27132895 | 2 |
| #27132894 | 2 |
| #27132700 | 2 |
| #27132658 | 2 |
| #467×C191 | 2 |
| #3050 | 191 |