Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×#63219 | C2 | semidirect |
| 2. C2×#10587610 | C2 | semidirect |
| 4. C2×#10587487 | C2 | semidirect |
| 5. C2×#10587492 | C2 | semidirect |
| 6. #11762572 | C2 | semidirect |
| 7. C2×C17×C22⋊C8 | C2 | semidirect |
| 56. C2×Dic34 | D4 | semidirect |
| 62. C2×C8×C17 | D4 | semidirect |
| 68. C4⋊Dic17 | D4 | semidirect |
| 77. C23×C17 | SD16 | semidirect |
| 154. C2×C22⋊C8 | D17 | semidirect |
| 186. C17 | #2000 | semidirect |
| 221. C2×C8 | C22⋊D17 | semidirect |
| 242. C23 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| C2×#10587610 | 2 |
| C2×#10587616 | 2 |
| C2×#10587487 | 2 |
| C2×#10587492 | 2 |
| #11762572 | 2 |
| C2×C17×C22⋊C8 | 2 |
| #2000 | 17 |