Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11763227 | C2 | semidirect |
| 2. #11763226 | C2 | semidirect |
| 4. #11762629 | C2 | semidirect |
| 5. #11762592 | C2 | semidirect |
| 6. #11762584 | C2 | semidirect |
| 7. C17×#350 | C2 | semidirect |
| 73. #350 | D17 | semidirect |
| 94. C17 | #2171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763227 | 2 |
| #11763226 | 2 |
| #11762924 | 2 |
| #11762629 | 2 |
| #11762592 | 2 |
| #11762584 | 2 |
| C17×#350 | 2 |
| #2171 | 17 |