Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10587628 | C2 | semidirect |
| 3. C2×#10587476 | C2 | semidirect |
| 4. #11762818 | C2 | semidirect |
| 5. C2×#10587504 | C2 | semidirect |
| 6. #11762569 | C2 | semidirect |
| 7. C2×C17×#124 | C2 | semidirect |
| 35. C2×Q8×C17 | D4 | semidirect |
| 56. C42×C17 | D4 | semidirect |
| 66. #63223 | D4 | semidirect |
| 128. C2×#124 | D17 | semidirect |
| 160. C17 | #2004 | semidirect |
| 172. C2×Q8 | C22⋊D17 | semidirect |
| 200. C42 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| #11763376 | 2 |
| C2×#10587476 | 2 |
| #11762818 | 2 |
| C2×#10587504 | 2 |
| #11762569 | 2 |
| C2×C17×#124 | 2 |
| #2004 | 17 |