Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#15690275 | C2 | semidirect |
| 2. C2×#20259329 | C2 | semidirect |
| 3. #27133234 | C2 | semidirect |
| 4. #27132907 | C2 | semidirect |
| 5. #27132890 | C2 | semidirect |
| 6. #27132699 | C2 | semidirect |
| 7. #27132671 | C2 | semidirect |
| 8. #27132668 | C2 | semidirect |
| 16. C2×#15690271 | C22 | semidirect |
| 18. C22×C191⋊C8 | C22 | semidirect |
| 22. #20259301 | C22 | semidirect |
| 24. #20259255 | C22 | semidirect |
| 25. #20259253 | C22 | semidirect |
| 26. #20259245 | C22 | semidirect |
| 45. C2×C191⋊C8 | D4 | semidirect |
| 120. C191 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690275 | 2 |
| C2×#20259329 | 2 |
| #27133234 | 2 |
| #27132907 | 2 |
| #27132890 | 2 |
| #27132699 | 2 |
| #27132671 | 2 |
| #27132668 | 2 |
| #535×C191 | 2 |
| #3057 | 191 |