Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11763575 | C2 | semidirect |
| 3. #11762791 | C2 | semidirect |
| 4. #11762773 | C2 | semidirect |
| 5. #11762581 | C2 | semidirect |
| 6. #11762580 | C2 | semidirect |
| 7. C17×#407 | C2 | semidirect |
| 50. C2×C8×C17 | D4 | semidirect |
| 62. C2×#3622 | D4 | semidirect |
| 124. #407 | D17 | semidirect |
| 152. C17 | #1891 | semidirect |
| 184. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763575 | 2 |
| #11763320 | 2 |
| #11762791 | 2 |
| #11762773 | 2 |
| #11762581 | 2 |
| #11762580 | 2 |
| C17×#407 | 2 |
| #1891 | 17 |