Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27132967 | C2 | semidirect |
| 4. #27132870 | C2 | semidirect |
| 6. #27132768 | C2 | semidirect |
| 7. C4×#15690277 | C2 | semidirect |
| 95. C191 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133140 | 2 |
| #27133001 | 2 |
| #27132967 | 2 |
| #27132870 | 2 |
| #27132818 | 2 |
| #27132768 | 2 |
| C4×#15690277 | 2 |
| #27132724 | 2 |
| #541×C191 | 2 |
| #3127 | 191 |