Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259345 | C2 | semidirect |
| 2. C2×#20259343 | C2 | semidirect |
| 3. C2×#20259341 | C2 | semidirect |
| 4. #27133212 | C2 | semidirect |
| 5. #27133047 | C2 | semidirect |
| 6. #27133045 | C2 | semidirect |
| 7. #27133041 | C2 | semidirect |
| 8. #27133038 | C2 | semidirect |
| 9. #27133034 | C2 | semidirect |
| 10. C4×C8×D191 | C2 | semidirect |
| 11. #495×C191 | C2 | semidirect |
| 62. C8×D191 | D4 | semidirect |
| 63. C8×D191 | D4 | semidirect |
| 119. Dic191 | #135 | semidirect |
| 125. C191 | #3147 | semidirect |
| 133. #495 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259345 | 2 |
| C2×#20259343 | 2 |
| C2×#20259341 | 2 |
| #27133212 | 2 |
| #27133047 | 2 |
| #27133045 | 2 |
| #27133041 | 2 |
| #27133038 | 2 |
| #27133034 | 2 |
| C4×C8×D191 | 2 |
| #495×C191 | 2 |
| #3147 | 191 |