Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
154 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 69 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 | C22×D317 |
| commutator | C22×C317 | C22×C4 |
| Fitting | #95×C317 | C2 |
| socle, prime radical, cosocle | C23×C317 | C23 |
| hypercenter | #95 | D317 |
| hypocenter | C317 | #387 |
| LCS | G ▷ C22×C317 ▷ C317 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C4⋊Dic317 | C4 | semidirect |
| 61. C317 | #387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic317 | 2 |
| C2×#19099553 | 2 |
| C2×C4×Dic317 | 2 |
| #23778687 | 2 |
| #95×C317 | 2 |
| #387 | 317 |