Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C2×#10587534 | C2 | semidirect |
| 3. #11763683 | C2 | semidirect |
| 8. C22×C8×C17 | C4 | semidirect |
| 9. C22×#3622 | C4 | semidirect |
| 11. C2×C8×D17 | C4 | semidirect |
| 12. C2×C8×D17 | C4 | semidirect |
| 64. C8×C17 | C22⋊C4 | semidirect |
| 66. #3622 | C22⋊C4 | semidirect |
| 70. C22×C17 | #107 | semidirect |
| 76. C2×D17 | #107 | semidirect |
| 105. C22×C8 | #595 | semidirect |
| 110. C17 | #1808 | semidirect |
| 160. C8 | C22⋊#595 | semidirect |
| 172. C22 | #10587534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587534 | 2 |
| #11763751 | 2 |
| #11763683 | 2 |
| C22×C8×D17 | 2 |
| #1808 | 17 |