Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26039206 | C2 | semidirect |
| 2. #26038456 | C2 | semidirect |
| 3. #26038435 | C2 | semidirect |
| 4. #26038406 | C2 | semidirect |
| 5. #26038211 | C2 | semidirect |
| 6. #26038203 | C2 | semidirect |
| 22. #137×C179 | C4 | semidirect |
| 24. AGL(1,ℤ/8)×C179 | C4 | semidirect |
| 118. C179 | #1881 | semidirect |
| 130. #137 | Dic179 | semidirect |
| 132. AGL(1,ℤ/8) | Dic179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039206 | 2 |
| #26038456 | 2 |
| #26038435 | 2 |
| #26038406 | 2 |
| #26038211 | 2 |
| #26038203 | 2 |
| #575×C179 | 2 |
| #1881 | 179 |