Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 194 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. #11763831 | C2 | direct (N × H) |
| 2. C2×C4⋊#3624 | C2 | semidirect |
| 4. C2×#10587542 | C2 | semidirect |
| 17. #10587542 | C22 | semidirect |
| 18. C4⋊#3624 | C22 | semidirect |
| 85. C2×C17 | #432 | semidirect |
| 103. C17 | C2×#432 | semidirect |
| 165. C2 | #11763831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763831 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×#10587543 | 2 |
| C2×#10587542 | 2 |
| C2×C42×D17 | 2 |
| C2×#432 | 17 |