Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#20259344 | C2 | semidirect |
| 2. C2×#20259342 | C2 | semidirect |
| 3. #27133209 | C2 | semidirect |
| 4. #27133048 | C2 | semidirect |
| 5. #27133046 | C2 | semidirect |
| 6. #27133044 | C2 | semidirect |
| 7. #27133041 | C2 | semidirect |
| 8. #27133038 | C2 | semidirect |
| 9. #27133034 | C2 | semidirect |
| 10. C2×C8×Dic191 | C2 | semidirect |
| 11. C2×#135×C191 | C2 | semidirect |
| 55. C2×C191⋊C8 | D4 | semidirect |
| 74. C2×C8×C191 | D4 | semidirect |
| 119. Dic191 | #135 | semidirect |
| 125. C191 | #3147 | semidirect |
| 129. C2×#135 | D191 | semidirect |
| 194. C2×C8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259344 | 2 |
| C2×#20259342 | 2 |
| #27133209 | 2 |
| #27133048 | 2 |
| #27133046 | 2 |
| #27133044 | 2 |
| #27133041 | 2 |
| #27133038 | 2 |
| #27133034 | 2 |
| C2×C8×Dic191 | 2 |
| C2×#135×C191 | 2 |
| #3147 | 191 |