Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
528 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 191 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. (C2×#3633)⋊C4 | C2 | direct (N × H) |
| 8. C22×#3633 | C4 | semidirect |
| 17. C22×#595 | C8 | semidirect |
| 28. C2×#3633 | C2×C4 | semidirect |
| 29. C22×C4×C17 | C8 | semidirect |
| 30. C22×Dic17 | C8 | semidirect |
| 33. C2×C4×D17 | C8 | semidirect |
| 54. C2×#595 | C2×C8 | semidirect |
| 61. C2×C4×C17 | C2×C8 | semidirect |
| 63. C2×Dic17 | C2×C8 | semidirect |
| 94. C2×C17 | #336 | semidirect |
| 98. D17 | #336 | semidirect |
| 113. C17 | C2×#336 | semidirect |
| 130. C22×C4 | #3633 | semidirect |
| 165. C2×C4 | C2×#3633 | semidirect |
| 195. C2 | (C2×#3633)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3633 | 2 |
| (C2×#3633)⋊C4 | 2 |
| C22×C4×#595 | 2 |
| C2×#336 | 17 |