Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 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×D136 | C2 | semidirect |
| 2. C2×#10587616 | C2 | semidirect |
| 3. C2×#10587492 | C2 | semidirect |
| 4. #11762572 | C2 | semidirect |
| 5. C2×C17×C22⋊C8 | C2 | semidirect |
| 36. C2×D68 | D4 | semidirect |
| 40. C2×C8×C17 | D4 | semidirect |
| 43. C4⋊Dic17 | D4 | semidirect |
| 49. C23×C17 | D8 | semidirect |
| 103. C2×C22⋊C8 | D17 | semidirect |
| 125. C17 | #1999 | semidirect |
| 148. C2×C8 | C22⋊D17 | semidirect |
| 163. C23 | D136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D136 | 2 |
| C2×#10587616 | 2 |
| C2×#10587492 | 2 |
| #11762572 | 2 |
| C2×C17×C22⋊C8 | 2 |
| #1999 | 17 |