Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D17 |
| commutator, cosocle | C16×C17 | C23 |
| Frattini | C16 | C22×D17 |
| Fitting | C17×SD64 | C2 |
| socle | C2×C17 | C2×D16 |
| hypercenter | SD64 | D17 |
| hypocenter | C17 | #2262 |
| LCS | G ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763242 | C2 | semidirect |
| 2. #11763238 | C2 | semidirect |
| 3. #11762649 | C2 | semidirect |
| 4. #11762648 | C2 | semidirect |
| 5. #11762644 | C2 | semidirect |
| 6. C32×D17 | C2 | semidirect |
| 7. C17×SD64 | C2 | semidirect |
| 53. SD64 | D17 | semidirect |
| 71. C17 | #2262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763242 | 2 |
| #11763238 | 2 |
| #11762649 | 2 |
| #11762648 | 2 |
| #11762644 | 2 |
| C32×D17 | 2 |
| C17×SD64 | 2 |
| #2262 | 17 |