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 |
|---|---|---|
| 2. #27132955 | C2 | semidirect |
| 3. #27132950 | C2 | semidirect |
| 4. #27132945 | C2 | semidirect |
| 5. #27132940 | C2 | semidirect |
| 6. #27132703 | C2 | semidirect |
| 7. #27132687 | C2 | semidirect |
| 9. C2×C4⋊Q8×C191 | C2 | semidirect |
| 36. #15690287 | Q8 | semidirect |
| 72. Dic382 | C2×Q8 | semidirect |
| 74. D764 | C2×Q8 | semidirect |
| 121. C191 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15690287 | 2 |
| #27132955 | 2 |
| #27132950 | 2 |
| #27132945 | 2 |
| #27132940 | 2 |
| #27132703 | 2 |
| #27132687 | 2 |
| #27132662 | 2 |
| C2×C4⋊Q8×C191 | 2 |
| #3079 | 191 |