Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 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. #27133370 | C2 | semidirect |
| 2. #27133035 | C2 | semidirect |
| 3. #27132860 | C2 | semidirect |
| 4. #27132411 | C2 | semidirect |
| 5. #27132393 | C2 | semidirect |
| 6. D4⋊(C191⋊C8) | C2 | semidirect |
| 67. D4×C191 | SD16 | semidirect |
| 96. C191 | #1622 | semidirect |
| 158. D4 | #15690275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133370 | 2 |
| #27133035 | 2 |
| #27132860 | 2 |
| #27132411 | 2 |
| #27132393 | 2 |
| D4⋊(C191⋊C8) | 2 |
| #459×C191 | 2 |
| #1622 | 191 |