Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763544 | C2 | semidirect |
| 2. #11763171 | C2 | semidirect |
| 3. #11763157 | C2 | semidirect |
| 4. #11763096 | C2 | semidirect |
| 5. #11763091 | C2 | semidirect |
| 6. #11763024 | C2 | semidirect |
| 8. #11762940 | C2 | semidirect |
| 9. #11762919 | C2 | semidirect |
| 10. C4×#63229 | C2 | semidirect |
| 11. D4×Q8×C17 | C2 | semidirect |
| 121. D4×Q8 | D17 | semidirect |
| 165. C17 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763171 | 2 |
| #11763157 | 2 |
| #11763096 | 2 |
| #11763091 | 2 |
| #11763024 | 2 |
| #11763004 | 2 |
| #11762940 | 2 |
| #11762919 | 2 |
| C4×#63229 | 2 |
| D4×Q8×C17 | 2 |
| #3373 | 17 |