Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#10587605 | C2 | semidirect |
| 2. #11763462 | C2 | semidirect |
| 3. #11763047 | C2 | semidirect |
| 4. #11763011 | C2 | semidirect |
| 5. #11762970 | C2 | semidirect |
| 6. C4×D136 | C2 | semidirect |
| 7. C8×D68 | C2 | semidirect |
| 8. C17×#494 | C2 | semidirect |
| 53. D136 | D4 | semidirect |
| 86. C4×C17 | #135 | semidirect |
| 93. #494 | D17 | semidirect |
| 124. C17 | #3283 | semidirect |
| 183. C4 | #10587605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587605 | 2 |
| #11763462 | 2 |
| #11763047 | 2 |
| #11763011 | 2 |
| #11762970 | 2 |
| C4×D136 | 2 |
| C8×D68 | 2 |
| C17×#494 | 2 |
| #3283 | 17 |