Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
836 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting, prime radical | C22×#41×C17 | C2 |
| hypercenter | C22×#41 | D17 |
| hypocenter | C17 | #2432 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587630 | C2 | semidirect |
| 2. C2×#10587622 | C2 | semidirect |
| 3. C2×#10587610 | C2 | semidirect |
| 4. #11762723 | C2 | semidirect |
| 5. #11762716 | C2 | semidirect |
| 6. #11762712 | C2 | semidirect |
| 7. #11762682 | C2 | semidirect |
| 8. C4×C22⋊Dic17 | C2 | semidirect |
| 105. C2×Dic17 | #41 | semidirect |
| 169. C17 | #2432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587630 | 2 |
| C2×#10587622 | 2 |
| C2×#10587610 | 2 |
| #11762723 | 2 |
| #11762716 | 2 |
| #11762712 | 2 |
| #11762682 | 2 |
| C4×C22⋊Dic17 | 2 |
| C22×#41×C17 | 2 |
| #2432 | 17 |