Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
160 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 47 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×#19153057 | C2 | semidirect |
| 2. C2×#19153052 | C2 | semidirect |
| 3. #26038681 | C2 | semidirect |
| 5. #26038264 | C2 | semidirect |
| 6. #26038244 | C2 | semidirect |
| 7. #357×C179 | C2 | semidirect |
| 33. C179⋊C16 | D4 | semidirect |
| 75. C179 | #2220 | semidirect |
| 83. #357 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153057 | 2 |
| C2×#19153052 | 2 |
| #26038681 | 2 |
| #26038672 | 2 |
| #26038264 | 2 |
| #26038244 | 2 |
| #357×C179 | 2 |
| #2220 | 179 |