Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
528 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 234 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. #11763827 | C2 | direct (N × H) |
| 2. C2×#10587544 | C2 | semidirect |
| 4. C2×C4×#3624 | C2 | semidirect |
| 16. #10587544 | C22 | semidirect |
| 18. C4×#3624 | C22 | semidirect |
| 28. C2×C4×D17 | C8 | semidirect |
| 62. C4×D17 | C2×C8 | semidirect |
| 85. C2×C17 | #431 | semidirect |
| 103. C17 | C2×#431 | semidirect |
| 165. C2 | #11763827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763827 | 2 |
| C2×#10587544 | 2 |
| C2×#10587543 | 2 |
| C2×C4×#3624 | 2 |
| C2×C42×D17 | 2 |
| C2×#431 | 17 |