Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #27132723 | C2 | semidirect |
| 3. #27132687 | C2 | semidirect |
| 5. M16×Dic191 | C2 | semidirect |
| 6. #423×C191 | C2 | semidirect |
| 14. C4⋊(C191⋊C8) | C22 | semidirect |
| 16. #20259232 | C22 | semidirect |
| 17. C8×Dic191 | C22 | semidirect |
| 20. C4⋊C8×C191 | C22 | semidirect |
| 75. C191 | #2921 | semidirect |
| 80. #423 | D191 | semidirect |
| 93. C4⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259279 | 2 |
| #27132723 | 2 |
| #27132687 | 2 |
| #27132626 | 2 |
| M16×Dic191 | 2 |
| #423×C191 | 2 |
| #2921 | 191 |