Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 436 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. #11763360 | C2 | semidirect |
| 2. #11763356 | C2 | semidirect |
| 3. #11763088 | C2 | semidirect |
| 4. #11763086 | C2 | semidirect |
| 5. #11763046 | C2 | semidirect |
| 6. #11763044 | C2 | semidirect |
| 7. #11763005 | C2 | semidirect |
| 8. #11763004 | C2 | semidirect |
| 9. #11763003 | C2 | semidirect |
| 10. C4⋊C8×D17 | C2 | semidirect |
| 11. C17×#474 | C2 | semidirect |
| 116. C4×D17 | D8 | semidirect |
| 148. #474 | D17 | semidirect |
| 193. C17 | #3245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763360 | 2 |
| #11763356 | 2 |
| #11763088 | 2 |
| #11763086 | 2 |
| #11763046 | 2 |
| #11763044 | 2 |
| #11763005 | 2 |
| #11763004 | 2 |
| #11763003 | 2 |
| C4⋊C8×D17 | 2 |
| C17×#474 | 2 |
| #3245 | 17 |