Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 228 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. #26012540 | C2 | semidirect |
| 2. Q8×#13063443 | C2 | semidirect |
| 20. D173⋊C8 | Q8 | direct (N × H) |
| 24. Q8×D173 | C8 | semidirect |
| 37. #13063443 | C2×Q8 | semidirect |
| 39. Dic346 | C2×C8 | semidirect |
| 47. Q8×C173 | C2×C8 | semidirect |
| 65. D173 | C8×Q8 | semidirect |
| 66. C173 | C2×C8×Q8 | semidirect |
| 105. Q8 | D173⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012540 | 2 |
| Q8×#13063443 | 2 |
| D173⋊(C4⋊C8) | 2 |
| C4×D173⋊C8 | 2 |
| C4×Q8×D173 | 2 |
| C2×C8×Q8 | 173 |