Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 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×#20259348 | C2 | semidirect |
| 2. #27133213 | C2 | semidirect |
| 3. #27132878 | C2 | semidirect |
| 4. #27132868 | C2 | semidirect |
| 5. #27132858 | C2 | semidirect |
| 6. #27132687 | C2 | semidirect |
| 7. #27132662 | C2 | semidirect |
| 8. C2×C4×D4×C191 | C2 | semidirect |
| 14. #20259322 | C22 | semidirect |
| 15. #20259319 | C22 | semidirect |
| 16. #20259310 | C22 | semidirect |
| 21. C4⋊(C191⋊C8) | C22 | semidirect |
| 22. C4⋊(C191⋊C8) | C22 | semidirect |
| 23. #20259245 | C22 | semidirect |
| 24. #20259242 | C22 | semidirect |
| 53. C2×D4×C191 | D4 | semidirect |
| 119. C4×C191 | AGL(1,ℤ/8) | semidirect |
| 129. C191 | #3036 | semidirect |
| 133. C2×C4×D4 | D191 | semidirect |
| 174. C2×D4 | D764 | semidirect |
| 250. C4 | #20259348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259348 | 2 |
| #27133213 | 2 |
| #27132878 | 2 |
| #27132868 | 2 |
| #27132858 | 2 |
| #27132687 | 2 |
| #27132662 | 2 |
| C2×C4×D4×C191 | 2 |
| #3036 | 191 |