Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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. #26012519 | C2 | semidirect |
| 2. D4×#13063443 | C2 | semidirect |
| 3. #26012353 | C2 | semidirect |
| 4. #26012339 | C2 | semidirect |
| 5. D4⋊#13063443 | C2 | semidirect |
| 6. #26012332 | C2 | semidirect |
| 33. #14583811 | C8 | semidirect |
| 49. D692 | C2×C8 | semidirect |
| 57. #13063436 | C2×C8 | semidirect |
| 60. D4×C173 | C2×C8 | semidirect |
| 83. C173 | #1580 | semidirect |
| 131. D4 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012519 | 2 |
| D4×#13063443 | 2 |
| #26012353 | 2 |
| #26012339 | 2 |
| D4⋊#13063443 | 2 |
| #26012332 | 2 |
| #26011571 | 2 |
| #1580 | 173 |