Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #11763219 | C2 | semidirect |
| 3. #11763216 | C2 | semidirect |
| 4. #11763214 | C2 | semidirect |
| 5. #11763213 | C2 | semidirect |
| 6. #11763210 | C2 | semidirect |
| 11. C17×#499 | C2 | semidirect |
| 66. #63218 | Q8 | semidirect |
| 67. C8×D17 | Q8 | semidirect |
| 110. #499 | D17 | semidirect |
| 146. C17 | #3164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763439 | 2 |
| #11763219 | 2 |
| #11763216 | 2 |
| #11763214 | 2 |
| #11763213 | 2 |
| #11763210 | 2 |
| #11762848 | 2 |
| #11762846 | 2 |
| #107×D17 | 2 |
| #11762763 | 2 |
| C17×#499 | 2 |
| #3164 | 17 |