Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #11763366 | C2 | semidirect |
| 2. #11763099 | C2 | semidirect |
| 3. #11763091 | C2 | semidirect |
| 4. #11763036 | C2 | semidirect |
| 5. #11763014 | C2 | semidirect |
| 6. #11763006 | C2 | semidirect |
| 7. C2×C4⋊#3622 | C2 | semidirect |
| 77. C2×C4×C17 | SD16 | semidirect |
| 145. C17 | #3246 | semidirect |
| 195. C2×C4 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763099 | 2 |
| #11763091 | 2 |
| #11763036 | 2 |
| #11763014 | 2 |
| #11763006 | 2 |
| C2×C4⋊#3622 | 2 |
| C17×#532 | 2 |
| #3246 | 17 |