Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763525 | C2 | semidirect |
| 2. #11763463 | C2 | semidirect |
| 3. #11763161 | C2 | semidirect |
| 4. #11763153 | C2 | semidirect |
| 5. #11763039 | C2 | semidirect |
| 6. #11763015 | C2 | semidirect |
| 7. #11762955 | C2 | semidirect |
| 8. C4×#63228 | C2 | semidirect |
| 9. #11762874 | C2 | semidirect |
| 10. #11762802 | C2 | semidirect |
| 11. C17×#476 | C2 | semidirect |
| 129. #476 | D17 | semidirect |
| 171. C17 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763525 | 2 |
| #11763463 | 2 |
| #11763161 | 2 |
| #11763153 | 2 |
| #11763039 | 2 |
| #11763015 | 2 |
| #11762955 | 2 |
| C4×#63228 | 2 |
| #11762874 | 2 |
| #11762802 | 2 |
| C17×#476 | 2 |
| #3303 | 17 |