Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 170 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. #11763859 | C2 | semidirect |
| 3. #11763858 | C2 | semidirect |
| 4. Q8×#3624 | C2 | semidirect |
| 44. #63242 | Q8 | semidirect |
| 126. C17 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763860 | 2 |
| #11763859 | 2 |
| #11763858 | 2 |
| Q8×#3624 | 2 |
| #11763816 | 2 |
| #11763813 | 2 |
| #11763774 | 2 |
| C4×#63242 | 2 |
| #11763364 | 2 |
| #2960 | 17 |