Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #26012355 | C2 | semidirect |
| 4. #26012354 | C2 | semidirect |
| 5. #26012353 | C2 | semidirect |
| 6. #26012352 | C2 | semidirect |
| 32. #14583809 | C8 | semidirect |
| 55. #13063436 | C2×C8 | semidirect |
| 60. C8×C173 | C2×C8 | semidirect |
| 77. C173 | #1565 | semidirect |
| 138. C8 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012510 | 2 |
| D173⋊(C4⋊C8) | 2 |
| #26012355 | 2 |
| #26012354 | 2 |
| #26012353 | 2 |
| #26012352 | 2 |
| #26011443 | 2 |
| #1565 | 173 |