Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#20259353 | C2 | semidirect |
| 3. #27132885 | C2 | semidirect |
| 4. #27132873 | C2 | semidirect |
| 5. #27132863 | C2 | semidirect |
| 6. #27132687 | C2 | semidirect |
| 7. #27132662 | C2 | semidirect |
| 8. C2×C4×Q8×C191 | C2 | semidirect |
| 52. C2×Q8×C191 | D4 | semidirect |
| 111. C4×C191 | #137 | semidirect |
| 120. C191 | #3037 | semidirect |
| 124. C2×C4×Q8 | D191 | semidirect |
| 160. C2×Q8 | D764 | semidirect |
| 233. C4 | #20259353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259353 | 2 |
| #27133213 | 2 |
| #27132885 | 2 |
| #27132873 | 2 |
| #27132863 | 2 |
| #27132687 | 2 |
| #27132662 | 2 |
| C2×C4×Q8×C191 | 2 |
| #3037 | 191 |