Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
234 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 79 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×#19150716 | C2 | semidirect |
| 4. #26014899 | C2 | semidirect |
| 5. #95×C353 | C2 | semidirect |
| 10. C2×C4×D353 | C4 | semidirect |
| 41. C2×D353 | C4⋊C4 | semidirect |
| 45. Dic353 | C22⋊C4 | semidirect |
| 52. C353 | #380 | semidirect |
| 58. #95 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D353 | 2 |
| C2×#19150716 | 2 |
| C2×#19150714 | 2 |
| #26014899 | 2 |
| #95×C353 | 2 |
| #380 | 353 |