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. #27133208 | C2 | semidirect |
| 2. #27133067 | C2 | semidirect |
| 3. #27133038 | C2 | semidirect |
| 4. #27133008 | C2 | semidirect |
| 5. #27132899 | C2 | semidirect |
| 6. #27132897 | C2 | semidirect |
| 7. D8×Dic191 | C2 | semidirect |
| 8. #27132745 | C2 | semidirect |
| 9. #27132743 | C2 | semidirect |
| 10. C2×C8×Dic191 | C2 | semidirect |
| 11. #466×C191 | C2 | semidirect |
| 82. C2×Dic191 | D8 | semidirect |
| 89. C191⋊C8 | #41 | semidirect |
| 101. C8×C191 | #41 | semidirect |
| 127. C191 | #3169 | semidirect |
| 135. #466 | D191 | semidirect |
| 229. C8 | #15690286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133208 | 2 |
| #27133067 | 2 |
| #27133038 | 2 |
| #27133008 | 2 |
| #27132899 | 2 |
| #27132897 | 2 |
| D8×Dic191 | 2 |
| #27132745 | 2 |
| #27132743 | 2 |
| C2×C8×Dic191 | 2 |
| #466×C191 | 2 |
| #3169 | 191 |