Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 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. C4×#63256 | C2 | semidirect |
| 3. #11763136 | C2 | semidirect |
| 4. #11763096 | C2 | semidirect |
| 5. #11763009 | C2 | semidirect |
| 6. #11763005 | C2 | semidirect |
| 7. #11762957 | C2 | semidirect |
| 8. #11762894 | C2 | semidirect |
| 9. #11762891 | C2 | semidirect |
| 10. #11762861 | C2 | semidirect |
| 11. C17×#477 | C2 | semidirect |
| 88. Q8×C17 | #41 | semidirect |
| 106. D68 | #41 | semidirect |
| 142. #477 | D17 | semidirect |
| 187. C17 | #3106 | semidirect |
| 233. Q8 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763360 | 2 |
| C4×#63256 | 2 |
| #11763136 | 2 |
| #11763096 | 2 |
| #11763009 | 2 |
| #11763005 | 2 |
| #11762957 | 2 |
| #11762894 | 2 |
| #11762891 | 2 |
| #11762861 | 2 |
| C17×#477 | 2 |
| #3106 | 17 |