Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. #27133061 | C2 | semidirect |
| 4. #27133036 | C2 | semidirect |
| 5. #27133014 | C2 | semidirect |
| 6. #27133010 | C2 | semidirect |
| 7. #27132892 | C2 | semidirect |
| 8. C4×#15690276 | C2 | semidirect |
| 9. C2×C4×C8×C191 | C2 | semidirect |
| 82. C2×C4×C191 | SD16 | semidirect |
| 90. C8×C191 | #41 | semidirect |
| 112. C191 | #3167 | semidirect |
| 122. C2×C4×C8 | D191 | semidirect |
| 195. C2×C4 | #15690276 | semidirect |
| 203. C8 | #15690287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| #27133213 | 2 |
| #27133061 | 2 |
| #27133036 | 2 |
| #27133014 | 2 |
| #27133010 | 2 |
| #27132892 | 2 |
| C4×#15690276 | 2 |
| C2×C4×C8×C191 | 2 |
| #3167 | 191 |