Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #26014925 | C2 | semidirect |
| 4. #26014916 | C2 | semidirect |
| 6. #26014903 | C2 | semidirect |
| 7. C4×Q8×C353 | C2 | semidirect |
| 10. #19150724 | C4 | semidirect |
| 26. #15667725 | C2×C4 | semidirect |
| 28. Q8×C353 | C2×C4 | semidirect |
| 49. C353 | #440 | semidirect |
| 52. C4×Q8 | D353 | semidirect |
| 72. Q8 | C4×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150724 | 2 |
| C4×D1412 | 2 |
| #26014925 | 2 |
| #26014916 | 2 |
| #26014912 | 2 |
| #26014903 | 2 |
| C4×Q8×C353 | 2 |
| #440 | 353 |