Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1008 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1008 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. C22×#63247 | C2 | semidirect |
| 2. #11763781 | C2 | direct (N × H) |
| 3. C2×#10587543 | C2 | semidirect |
| 14. C2×#63247 | C22 | semidirect |
| 15. C22×#3624 | C22 | semidirect |
| 16. #10587543 | C22 | semidirect |
| 39. C2×#3624 | C23 | semidirect |
| 49. C22×D17 | M16 | semidirect |
| 76. C2×D17 | C2×M16 | semidirect |
| 86. C2×C17 | #407 | semidirect |
| 102. C17 | C2×#407 | semidirect |
| 168. C2 | #11763781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| #11763781 | 2 |
| C2×#10587543 | 2 |
| C23×C4×D17 | 2 |
| C2×#407 | 17 |