Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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×#10587489 | C2 | semidirect |
| 4. #11762571 | C2 | semidirect |
| 5. C2×C17×#107 | C2 | semidirect |
| 14. C2×C8×D17 | C4 | semidirect |
| 68. C8×C17 | C22⋊C4 | semidirect |
| 84. C2×D17 | #107 | semidirect |
| 94. C2×#107 | D17 | semidirect |
| 117. C17 | #1808 | semidirect |
| 169. C8 | #63227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D17 | 2 |
| C2×#10587489 | 2 |
| #11762666 | 2 |
| #11762571 | 2 |
| C2×C17×#107 | 2 |
| #1808 | 17 |