Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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. C22×#15668243 | C2 | semidirect |
| 2. C2×#19153034 | C2 | semidirect |
| 3. #26038299 | C2 | semidirect |
| 4. #26038201 | C2 | semidirect |
| 17. #121×C179 | C4 | semidirect |
| 24. C2×C179⋊C8 | D4 | semidirect |
| 104. C179 | #1895 | semidirect |
| 118. #121 | Dic179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668243 | 2 |
| C2×#19153034 | 2 |
| #26038299 | 2 |
| #26038201 | 2 |
| C2×#121×C179 | 2 |
| #1895 | 179 |