Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27133035 | C2 | semidirect |
| 2. #27132958 | C2 | semidirect |
| 3. #27132953 | C2 | semidirect |
| 4. #27132407 | C2 | semidirect |
| 5. Q8⋊(C191⋊C8) | C2 | semidirect |
| 6. D4⋊(C191⋊C8) | C2 | semidirect |
| 58. Q8×C191 | SD16 | semidirect |
| 98. C191 | #1631 | semidirect |
| 153. Q8 | #15690275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133035 | 2 |
| #27132958 | 2 |
| #27132953 | 2 |
| #27132407 | 2 |
| Q8⋊(C191⋊C8) | 2 |
| D4⋊(C191⋊C8) | 2 |
| #550×C191 | 2 |
| #1631 | 191 |