Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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. D173⋊#108 | C2 | semidirect |
| 2. #26012483 | C2 | semidirect |
| 3. D173⋊#100 | C2 | semidirect |
| 4. #26012454 | C2 | semidirect |
| 16. C2×D1384 | C4 | semidirect |
| 17. C2×#14583811 | C4 | semidirect |
| 23. C2×D8×C173 | C4 | semidirect |
| 100. C173 | #1978 | semidirect |
| 114. C2×D8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#108 | 2 |
| #26012483 | 2 |
| D173⋊#100 | 2 |
| #26012454 | 2 |
| C2×D8×D173 | 2 |
| #1978 | 173 |