Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27133066 | C2 | semidirect |
| 3. #27133036 | C2 | semidirect |
| 4. #27133011 | C2 | semidirect |
| 5. #27133009 | C2 | semidirect |
| 6. C8×C191⋊C8 | C2 | semidirect |
| 7. #492×C191 | C2 | semidirect |
| 47. C191⋊C8 | SD16 | semidirect |
| 57. C8×C191 | D8 | semidirect |
| 75. C191 | #1706 | semidirect |
| 80. #492 | D191 | semidirect |
| 133. C8 | #15690272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133066 | 2 |
| #27133039 | 2 |
| #27133036 | 2 |
| #27133011 | 2 |
| #27133009 | 2 |
| C8×C191⋊C8 | 2 |
| #492×C191 | 2 |
| #1706 | 191 |