Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
852 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic382 | C2 | semidirect |
| 2. C2×#20259310 | C2 | semidirect |
| 4. #27132576 | C2 | semidirect |
| 5. #27132569 | C2 | semidirect |
| 6. #27132540 | C2 | semidirect |
| 7. C4×C22⋊C4×C191 | C2 | semidirect |
| 31. C2×Dic382 | D4 | semidirect |
| 81. C22×C191 | #124 | semidirect |
| 101. C191 | #2436 | semidirect |
| 109. C4×C22⋊C4 | D191 | semidirect |
| 187. C22 | #20259310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic382 | 2 |
| C2×#20259310 | 2 |
| C2×#20259296 | 2 |
| #27132576 | 2 |
| #27132569 | 2 |
| #27132540 | 2 |
| C4×C22⋊C4×C191 | 2 |
| #2436 | 191 |