Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. #11763651 | C2 | semidirect |
| 4. C8×#3624 | C2 | semidirect |
| 24. #63243 | C8 | semidirect |
| 44. #3624 | C2×C8 | semidirect |
| 45. #3624 | M16 | semidirect |
| 81. C17 | C8×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63243 | 2 |
| C4×#63242 | 2 |
| #11763651 | 2 |
| C8×#3624 | 2 |
| #11762861 | 2 |
| C8×M16 | 17 |