Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
412 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 164 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. #11763860 | C2 | semidirect |
| 2. #11763843 | C2 | semidirect |
| 3. #11763839 | C2 | semidirect |
| 4. #11763828 | C2 | semidirect |
| 5. #11763827 | C2 | semidirect |
| 6. C4×#63243 | C2 | semidirect |
| 7. C4×#63242 | C2 | semidirect |
| 79. C4×D17 | M16 | semidirect |
| 82. #3624 | #41 | semidirect |
| 135. C17 | #2965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763860 | 2 |
| #11763843 | 2 |
| #11763839 | 2 |
| #11763828 | 2 |
| #11763827 | 2 |
| C4×#63243 | 2 |
| C4×#63242 | 2 |
| C4×#63256 | 2 |
| #2965 | 17 |