Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27133210 | C2 | semidirect |
| 2. #27133067 | C2 | semidirect |
| 3. #27133038 | C2 | semidirect |
| 4. #27133008 | C2 | semidirect |
| 5. #27132900 | C2 | semidirect |
| 6. #27132898 | C2 | semidirect |
| 7. #27132896 | C2 | semidirect |
| 8. C4×D1528 | C2 | semidirect |
| 9. C4×#15690272 | C2 | semidirect |
| 10. C4×C8×D191 | C2 | semidirect |
| 11. C4×D8×C191 | C2 | semidirect |
| 89. C4×D191 | D8 | semidirect |
| 91. C191⋊C8 | #41 | semidirect |
| 101. C8×C191 | #41 | semidirect |
| 127. C191 | #3169 | semidirect |
| 138. C4×D8 | D191 | semidirect |
| 229. C8 | #15690287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133210 | 2 |
| #27133067 | 2 |
| #27133038 | 2 |
| #27133008 | 2 |
| #27132900 | 2 |
| #27132898 | 2 |
| #27132896 | 2 |
| C4×D1528 | 2 |
| C4×#15690272 | 2 |
| C4×C8×D191 | 2 |
| C4×D8×C191 | 2 |
| #3169 | 191 |