Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
216 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #3633 |
| commutator, hypocenter | C17 | C2×C4×C16 |
| Frattini | C4 | C22×#3633 |
| Fitting | C2×C8×C17 | C8 |
| socle | C22×C17 | C4×C8 |
| prime radical | C22×D17 | C2×C8 |
| cosocle | #63242 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11763902 | C2 | direct (N × H) |
| 6. C2×#63241 | C4 | semidirect |
| 7. #10587665 | C4 | semidirect |
| 20. #63241 | C2×C4 | semidirect |
| 26. C2×#595 | C16 | semidirect |
| 43. #595 | C2×C16 | semidirect |
| 51. C2×C17 | C4×C16 | semidirect |
| 53. D17 | C4×C16 | semidirect |
| 63. C17 | C2×C4×C16 | semidirect |
| 101. C2 | #11763902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587665 | 2 |
| #11763902 | 2 |
| C2×C8×#595 | 2 |
| C2×C4×C16 | 17 |