Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #27133071 | C2 | semidirect |
| 4. #27133070 | C2 | semidirect |
| 5. #27133065 | C2 | semidirect |
| 6. #27133062 | C2 | semidirect |
| 7. #27133062 | C2 | semidirect |
| 11. #499×C191 | C2 | semidirect |
| 43. #15690270 | Q8 | semidirect |
| 44. #15690270 | Q8 | semidirect |
| 99. C191 | #3166 | semidirect |
| 108. #499 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133219 | 2 |
| #125×D191 | 2 |
| #27133071 | 2 |
| #27133070 | 2 |
| #27133065 | 2 |
| #27133062 | 2 |
| #27132704 | 2 |
| #27132702 | 2 |
| C4×#15690270 | 2 |
| #499×C191 | 2 |
| #3166 | 191 |