Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11763828 | C2 | semidirect |
| 2. C4×C4⋊#595 | C2 | semidirect |
| 3. #11763661 | C2 | semidirect |
| 8. C17×C4⋊Q8 | C4 | semidirect |
| 13. #10587579 | C4 | semidirect |
| 14. #10587560 | C4 | semidirect |
| 95. C4⋊Q8 | #595 | semidirect |
| 109. C17 | #1502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763828 | 2 |
| C4×C4⋊#595 | 2 |
| #11763661 | 2 |
| #11763360 | 2 |
| #1502 | 17 |