Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763363 | C2 | semidirect |
| 3. #11763098 | C2 | semidirect |
| 4. #11763091 | C2 | semidirect |
| 5. #11763041 | C2 | semidirect |
| 6. #11763039 | C2 | semidirect |
| 7. #11763013 | C2 | semidirect |
| 8. #11763010 | C2 | semidirect |
| 9. #11763009 | C2 | semidirect |
| 10. C4⋊C8×D17 | C2 | semidirect |
| 11. C17×#475 | C2 | semidirect |
| 107. C4×D17 | SD16 | semidirect |
| 137. #475 | D17 | semidirect |
| 180. C17 | #3246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763363 | 2 |
| #11763360 | 2 |
| #11763098 | 2 |
| #11763091 | 2 |
| #11763041 | 2 |
| #11763039 | 2 |
| #11763013 | 2 |
| #11763010 | 2 |
| #11763009 | 2 |
| C4⋊C8×D17 | 2 |
| C17×#475 | 2 |
| #3246 | 17 |