Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #27133043 | C2 | semidirect |
| 3. #27133015 | C2 | semidirect |
| 5. #27132769 | C2 | semidirect |
| 7. #498×C191 | C2 | semidirect |
| 68. C191 | #3185 | semidirect |
| 71. #498 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #27133043 | 2 |
| #27133015 | 2 |
| #27132922 | 2 |
| #27132769 | 2 |
| C4×#15690270 | 2 |
| #498×C191 | 2 |
| #3185 | 191 |