Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
114 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×#19150727 | C2 | semidirect |
| 5. #26014925 | C2 | semidirect |
| 6. #26014917 | C2 | semidirect |
| 7. #103×C353 | C2 | semidirect |
| 39. C2×D353 | Q16 | semidirect |
| 51. C353 | #467 | semidirect |
| 59. #103 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150727 | 2 |
| C2×C8×D353 | 2 |
| #26014972 | 2 |
| #26014968 | 2 |
| #26014925 | 2 |
| #26014917 | 2 |
| #103×C353 | 2 |
| #467 | 353 |