Finite Group DatabasebetaFinite Group DatabasebetaOrder 832.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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×D13 |
| commutator, socle, cosocle | C23×C13 | C23 |
| Fitting | C2×C13×C4⋊C4 | C2 |
| prime radical | C23×D13 | C22 |
| hypercenter | C2×C4⋊C4 | D13 |
| hypocenter | C13 | #396 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×C4⋊C4 | C2 | semidirect |
| 5. C2×C4⋊Dic13 | C2 | semidirect |
| 6. C2×#6101 | C2 | semidirect |
| 7. #88071 | C2 | semidirect |
| 70. C2×C4⋊C4 | D13 | semidirect |
| 96. C13 | #396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C4⋊C4 | 2 |
| C2×#6103 | 2 |
| C2×C4⋊Dic13 | 2 |
| C2×#6101 | 2 |
| #88071 | 2 |
| #396 | 13 |