Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D353 | C2 | semidirect |
| 3. #26014990 | C2 | semidirect |
| 4. #26014981 | C2 | semidirect |
| 5. #26014980 | C2 | semidirect |
| 6. #26014977 | C2 | semidirect |
| 7. #26014970 | C2 | semidirect |
| 8. #26014949 | C2 | semidirect |
| 9. C4⋊Q8×C353 | C2 | semidirect |
| 63. C353 | #536 | semidirect |
| 68. C4⋊Q8 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150738 | 2 |
| C2×Q8×D353 | 2 |
| #26014990 | 2 |
| #26014981 | 2 |
| #26014980 | 2 |
| #26014977 | 2 |
| #26014970 | 2 |
| #26014949 | 2 |
| C4⋊Q8×C353 | 2 |
| #536 | 353 |