Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 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. #27133220 | C2 | semidirect |
| 2. #27133017 | C2 | semidirect |
| 3. #27133013 | C2 | semidirect |
| 4. #27133009 | C2 | semidirect |
| 5. #27132659 | C2 | semidirect |
| 6. C2×C4×C191⋊C8 | C2 | semidirect |
| 78. C191 | #3131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| #27133017 | 2 |
| #27133013 | 2 |
| #27133009 | 2 |
| #27132659 | 2 |
| C2×C4×C191⋊C8 | 2 |
| #532×C191 | 2 |
| #3131 | 191 |