Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27133013 | C2 | semidirect |
| 2. #27132943 | C2 | semidirect |
| 3. #27132868 | C2 | semidirect |
| 4. #27132412 | C2 | semidirect |
| 5. D4⋊(C191⋊C8) | C2 | semidirect |
| 6. D4⋊(C191⋊C8) | C2 | semidirect |
| 93. C191 | #1646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133013 | 2 |
| #27132943 | 2 |
| #27132868 | 2 |
| #27132412 | 2 |
| D4⋊(C191⋊C8) | 2 |
| #555×C191 | 2 |
| #1646 | 191 |