Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26038789 | C2 | semidirect |
| 3. #26038649 | C2 | semidirect |
| 4. #26038188 | C2 | semidirect |
| 5. Q8⋊(C179⋊C8) | C2 | semidirect |
| 59. D4×C179 | Q16 | semidirect |
| 88. C179 | #1644 | semidirect |
| 144. D4 | #15668249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038789 | 2 |
| #26038719 | 2 |
| #26038649 | 2 |
| #26038188 | 2 |
| Q8⋊(C179⋊C8) | 2 |
| D4⋊(C179⋊C8) | 2 |
| #554×C179 | 2 |
| #1644 | 179 |