Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11763011 | C2 | semidirect |
| 3. #11762888 | C2 | semidirect |
| 4. #11762560 | C2 | semidirect |
| 5. #11762555 | C2 | semidirect |
| 6. #11762553 | C2 | semidirect |
| 7. C17×#486 | C2 | semidirect |
| 80. #486 | D17 | semidirect |
| 107. C17 | #1701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763011 | 2 |
| #11763001 | 2 |
| #11762888 | 2 |
| #11762560 | 2 |
| #11762555 | 2 |
| #11762553 | 2 |
| C17×#486 | 2 |
| #1701 | 17 |