Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#20259346 | C2 | semidirect |
| 2. #27133211 | C2 | semidirect |
| 3. C4×D4×D191 | C2 | semidirect |
| 4. #27132877 | C2 | semidirect |
| 5. #27132876 | C2 | semidirect |
| 6. #27132869 | C2 | semidirect |
| 7. #27132868 | C2 | semidirect |
| 8. #27132855 | C2 | semidirect |
| 9. #27132685 | C2 | semidirect |
| 10. #27132661 | C2 | semidirect |
| 11. #459×C191 | C2 | semidirect |
| 20. #20259322 | C22 | semidirect |
| 21. #20259309 | C22 | semidirect |
| 34. C4⋊(C191⋊C8) | C22 | semidirect |
| 35. Dic191⋊C8 | C22 | semidirect |
| 36. #20259247 | C22 | semidirect |
| 37. #20259245 | C22 | semidirect |
| 38. #20259243 | C22 | semidirect |
| 40. #127×C191 | C22 | semidirect |
| 42. C4⋊C8×C191 | C22 | semidirect |
| 43. #102×C191 | C22 | semidirect |
| 52. D4×D191 | D4 | semidirect |
| 145. C4×C191 | AGL(1,ℤ/8) | semidirect |
| 160. C191 | #3036 | semidirect |
| 170. #459 | D191 | semidirect |
| 183. #127 | C2×D191 | semidirect |
| 200. C4⋊C8 | C2×D191 | semidirect |
| 204. #102 | C2×D191 | semidirect |
| 311. C4 | #20259346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259346 | 2 |
| #27133211 | 2 |
| C4×D4×D191 | 2 |
| #27132877 | 2 |
| #27132876 | 2 |
| #27132869 | 2 |
| #27132868 | 2 |
| #27132855 | 2 |
| #27132685 | 2 |
| #27132661 | 2 |
| #459×C191 | 2 |
| #3036 | 191 |