Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#19153058 | C2 | semidirect |
| 2. C2×#19153057 | C2 | semidirect |
| 4. #26038533 | C2 | semidirect |
| 5. Dic179⋊C16 | C2 | semidirect |
| 6. #26038239 | C2 | semidirect |
| 7. #357×C179 | C2 | semidirect |
| 26. Dic716 | D4 | semidirect |
| 71. Dic179 | SD32 | semidirect |
| 77. C179 | #2207 | semidirect |
| 85. #357 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153058 | 2 |
| C2×#19153057 | 2 |
| #26038814 | 2 |
| #26038533 | 2 |
| Dic179⋊C16 | 2 |
| #26038239 | 2 |
| #357×C179 | 2 |
| #2207 | 179 |