Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
112 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D17 |
| commutator, socle | C2×C17 | C22×C16 |
| Fitting | C17×M64 | C2 |
| prime radical | C22×D17 | C16 |
| cosocle | C16×C17 | C23 |
| hypercenter | M64 | D17 |
| hypocenter | C17 | C2×M64 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C16 ◁ M64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11762643 | C2 | semidirect |
| 3. #11762642 | C2 | semidirect |
| 4. C32×D17 | C2 | semidirect |
| 5. C17×M64 | C2 | semidirect |
| 13. C17×C32 | C22 | semidirect |
| 14. #10587465 | C22 | semidirect |
| 49. M64 | D17 | direct (N × H) |
| 54. D17 | M64 | direct (N × H) |
| 63. C32 | C2×D17 | semidirect |
| 64. C17 | C2×M64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D17 | 2 |
| #11762643 | 2 |
| #11762642 | 2 |
| C32×D17 | 2 |
| C17×M64 | 2 |
| C2×M64 | 17 |