Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #11762551 | C2 | semidirect |
| 4. #11762550 | C2 | semidirect |
| 5. C17×#330 | C2 | semidirect |
| 59. #330 | D17 | direct (N × H) |
| 62. D17 | #330 | direct (N × H) |
| 74. C17 | C2×#330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D17 | 2 |
| #97×D17 | 2 |
| #11762551 | 2 |
| #11762550 | 2 |
| C17×#330 | 2 |
| C2×#330 | 17 |