Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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. C4×Dic706 | C2 | semidirect |
| 3. #26014923 | C2 | semidirect |
| 4. #26014915 | C2 | semidirect |
| 6. C4×#15667725 | C2 | semidirect |
| 9. #19150725 | C4 | direct (N × H) |
| 21. Dic706 | C2×C4 | semidirect |
| 25. #15667725 | C2×C4 | semidirect |
| 40. C4×C353 | SD16 | semidirect |
| 49. C353 | C4×SD16 | semidirect |
| 92. C4 | #19150725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150725 | 2 |
| C4×Dic706 | 2 |
| #26014923 | 2 |
| #26014915 | 2 |
| #26014913 | 2 |
| C4×#15667725 | 2 |
| C4×D4×C353 | 2 |
| C4×SD16 | 353 |