Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26038560 | C2 | semidirect |
| 3. #26038551 | C2 | semidirect |
| 4. #26038263 | C2 | semidirect |
| 5. #26038250 | C2 | semidirect |
| 6. #26038216 | C2 | semidirect |
| 7. #361×C179 | C2 | semidirect |
| 11. #19153057 | C4 | semidirect |
| 12. #19153054 | C4 | semidirect |
| 23. Dic716 | C2×C4 | semidirect |
| 25. D1432 | C2×C4 | semidirect |
| 32. C179⋊C16 | C2×C4 | semidirect |
| 68. C179 | AGL(1,ℤ/16) | semidirect |
| 74. #361 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038875 | 2 |
| #26038560 | 2 |
| #26038551 | 2 |
| #26038263 | 2 |
| #26038250 | 2 |
| #26038216 | 2 |
| #361×C179 | 2 |
| AGL(1,ℤ/16) | 179 |