Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27132964 | C2 | semidirect |
| 4. #27132954 | C2 | semidirect |
| 5. #27132944 | C2 | semidirect |
| 6. #27132705 | C2 | semidirect |
| 8. #423×C191 | C2 | semidirect |
| 11. #20259322 | C22 | semidirect |
| 12. #20259322 | C22 | semidirect |
| 13. #20259314 | C22 | semidirect |
| 25. #20259256 | C22 | semidirect |
| 26. #20259254 | C22 | semidirect |
| 31. C4⋊C8×C191 | C22 | semidirect |
| 32. C4⋊C8×C191 | C22 | semidirect |
| 38. C2×D764 | Q8 | semidirect |
| 115. C191 | #3077 | semidirect |
| 123. #423 | D191 | semidirect |
| 145. C4⋊C8 | C2×D191 | semidirect |
| 146. C4⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| C2×C4×D764 | 2 |
| #27132964 | 2 |
| #27132954 | 2 |
| #27132944 | 2 |
| #27132705 | 2 |
| #27132669 | 2 |
| #423×C191 | 2 |
| #3077 | 191 |