Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #26011544 | C2 | semidirect |
| 3. #26011223 | C2 | semidirect |
| 4. #26011220 | C2 | semidirect |
| 5. C2×C4×C8×C173 | C2 | semidirect |
| 24. #14583826 | C8 | semidirect |
| 53. Dic346 | C2×C8 | semidirect |
| 55. D692 | C2×C8 | semidirect |
| 98. C173 | #1476 | semidirect |
| 102. C2×C4×C8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| #26011544 | 2 |
| #26011223 | 2 |
| #26011220 | 2 |
| C2×C4×C8×C173 | 2 |
| #1476 | 173 |