Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D191 | C2 | semidirect |
| 3. #27132958 | C2 | semidirect |
| 4. #27132954 | C2 | semidirect |
| 5. #27132950 | C2 | semidirect |
| 6. #27132946 | C2 | semidirect |
| 7. #27132942 | C2 | semidirect |
| 8. #27132704 | C2 | semidirect |
| 9. #27132685 | C2 | semidirect |
| 11. #477×C191 | C2 | semidirect |
| 44. #15690288 | Q8 | semidirect |
| 88. D764 | C2×Q8 | semidirect |
| 105. Q8×C191 | C2×Q8 | semidirect |
| 137. C191 | #3079 | semidirect |
| 142. #477 | D191 | semidirect |
| 226. Q8 | Q8×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D191 | 2 |
| C4×#15690288 | 2 |
| #27132958 | 2 |
| #27132954 | 2 |
| #27132950 | 2 |
| #27132946 | 2 |
| #27132942 | 2 |
| #27132704 | 2 |
| #27132685 | 2 |
| #27132663 | 2 |
| #477×C191 | 2 |
| #3079 | 191 |