Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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×#10587534 | C2 | semidirect |
| 3. C2×#10587533 | C2 | semidirect |
| 5. #11763683 | C2 | semidirect |
| 6. #11763683 | C2 | semidirect |
| 23. C17×C22⋊C8 | C4 | semidirect |
| 24. C22⋊#3622 | C4 | semidirect |
| 25. #10587491 | C4 | semidirect |
| 26. #10587491 | C4 | semidirect |
| 165. C22⋊C8 | #595 | semidirect |
| 167. C17 | #1854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| C2×#10587534 | 2 |
| C2×#10587533 | 2 |
| #11763751 | 2 |
| #11763683 | 2 |
| C22⋊C8×D17 | 2 |
| #1854 | 17 |