Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
168 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11762939 | C2 | semidirect |
| 4. #11762560 | C2 | semidirect |
| 5. #11762541 | C2 | semidirect |
| 7. C17×#322 | C2 | semidirect |
| 58. C8×C17 | SD16 | semidirect |
| 80. #322 | D17 | semidirect |
| 100. C17 | #1582 | semidirect |
| 138. C8 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762939 | 2 |
| C4×#63219 | 2 |
| C8×D68 | 2 |
| #11762560 | 2 |
| #11762541 | 2 |
| #11762538 | 2 |
| C17×#322 | 2 |
| #1582 | 17 |