Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#20259347 | C2 | semidirect |
| 2. C22×#15690274 | C2 | semidirect |
| 3. #27133227 | C2 | semidirect |
| 4. #27132808 | C2 | semidirect |
| 5. #27132802 | C2 | semidirect |
| 6. #27132672 | C2 | semidirect |
| 7. #27132659 | C2 | semidirect |
| 8. #27132630 | C2 | semidirect |
| 9. C2×2−1+4×C191 | C2 | semidirect |
| 23. #20259246 | C22 | semidirect |
| 24. #20259246 | C22 | semidirect |
| 25. #20259243 | C22 | semidirect |
| 26. C22⋊(C191⋊C8) | C22 | semidirect |
| 33. C2×#41×C191 | C22 | semidirect |
| 36. C22×Q8×C191 | C22 | semidirect |
| 61. #41×C191 | D4 | semidirect |
| 69. C2×Q8×C191 | D4 | semidirect |
| 145. C191 | #3010 | semidirect |
| 147. C2×2−1+4 | D191 | semidirect |
| 162. C2×#41 | C2×D191 | semidirect |
| 165. C22×Q8 | C2×D191 | semidirect |
| 191. #41 | C22⋊D191 | semidirect |
| 199. C2×Q8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259347 | 2 |
| C22×#15690274 | 2 |
| #27133227 | 2 |
| #27132808 | 2 |
| #27132802 | 2 |
| #27132672 | 2 |
| #27132659 | 2 |
| #27132630 | 2 |
| C2×2−1+4×C191 | 2 |
| #3010 | 191 |