Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
212 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 13. C2×#3633 | C8 | semidirect |
| 15. C2×#3624 | C8 | semidirect |
| 21. C2×C8×C17 | C8 | semidirect |
| 22. C2×#3622 | C8 | semidirect |
| 66. C17 | #1273 | semidirect |
| 78. C2×C8 | #3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#3633 | 2 |
| C2×C8×#595 | 2 |
| #1273 | 17 |