Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20259322 | C2 | semidirect |
| 3. #27132959 | C2 | semidirect |
| 4. #27132954 | C2 | semidirect |
| 5. #27132949 | C2 | semidirect |
| 6. #27132944 | C2 | semidirect |
| 7. #27132705 | C2 | semidirect |
| 9. #423×C191 | C2 | semidirect |
| 36. #15690287 | Q8 | semidirect |
| 74. Dic382 | C2×Q8 | semidirect |
| 76. D764 | C2×Q8 | semidirect |
| 121. C191 | #3079 | semidirect |
| 130. #423 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259322 | 2 |
| C4×#15690287 | 2 |
| #27132959 | 2 |
| #27132954 | 2 |
| #27132949 | 2 |
| #27132944 | 2 |
| #27132705 | 2 |
| #27132665 | 2 |
| #423×C191 | 2 |
| #3079 | 191 |