Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#20259348 | C2 | semidirect |
| 2. #27133213 | C2 | semidirect |
| 3. #27133050 | C2 | semidirect |
| 4. #27133039 | C2 | semidirect |
| 5. #27133035 | C2 | semidirect |
| 6. C4×#15690271 | C2 | semidirect |
| 7. C2×#127×C191 | C2 | semidirect |
| 10. C2×#15690275 | C22 | semidirect |
| 11. C2×#15690272 | C22 | semidirect |
| 13. #20259322 | C22 | semidirect |
| 14. #20259319 | C22 | semidirect |
| 15. #20259310 | C22 | semidirect |
| 18. #20259233 | C22 | semidirect |
| 19. C4×C191⋊C8 | C22 | semidirect |
| 34. #15690271 | D4 | semidirect |
| 57. C191⋊C8 | C2×D4 | semidirect |
| 82. C4×C191 | AGL(1,ℤ/8) | semidirect |
| 90. C191 | #3151 | semidirect |
| 94. C2×#127 | D191 | semidirect |
| 174. C4 | #20259348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259348 | 2 |
| #27133213 | 2 |
| #27133050 | 2 |
| #27133039 | 2 |
| #27133035 | 2 |
| C4×#15690271 | 2 |
| C2×#127×C191 | 2 |
| #3151 | 191 |