Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
276 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 72 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. #26012494 | C2 | semidirect |
| 2. C2×C4×#13063443 | C2 | semidirect |
| 3. #26012339 | C2 | semidirect |
| 4. D4⋊#13063443 | C2 | semidirect |
| 105. C173 | #1492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012494 | 2 |
| C2×C4×#13063443 | 2 |
| #26012339 | 2 |
| D4⋊#13063443 | 2 |
| #26012036 | 2 |
| #1492 | 173 |