Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
328 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #11763895 | C2 | direct (N × H) |
| 26. C22×C4×C17 | C8 | semidirect |
| 27. C22×Dic17 | C8 | semidirect |
| 32. C2×C4×D17 | C8 | semidirect |
| 58. C2×C4×C17 | C2×C8 | semidirect |
| 61. C2×Dic17 | C2×C8 | semidirect |
| 94. C2×C17 | #324 | semidirect |
| 98. D17 | #324 | semidirect |
| 111. C17 | C2×#324 | semidirect |
| 129. C22×C4 | #3633 | semidirect |
| 162. C2×C4 | C2×#3633 | semidirect |
| 193. C2 | #11763895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#3633 | 2 |
| #11763895 | 2 |
| C22×C4⋊#595 | 2 |
| C2×#324 | 17 |