Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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×#10587498 | C2 | semidirect |
| 3. #11763193 | C2 | semidirect |
| 4. C4⋊#63214 | C2 | semidirect |
| 5. #11762612 | C2 | semidirect |
| 6. #11762609 | C2 | semidirect |
| 7. C4×D8×C17 | C2 | semidirect |
| 75. C4×D8 | D17 | semidirect |
| 97. C17 | #2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587498 | 2 |
| C2×#10587497 | 2 |
| #11763193 | 2 |
| C4⋊#63214 | 2 |
| #11762612 | 2 |
| #11762609 | 2 |
| C4×D8×C17 | 2 |
| #2210 | 17 |