Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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×D53 |
| commutator, socle, cosocle | C23×C53 | C23 |
| Fitting | C2×C4⋊C4×C53 | C2 |
| prime radical | C23×D53 | C22 |
| hypercenter | C2×C4⋊C4 | D53 |
| hypocenter | C53 | #399 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11719919 | C2 | semidirect |
| 4. #13133124 | C2 | semidirect |
| 5. C2×C4⋊C4×C53 | C2 | semidirect |
| 52. C53 | #399 | semidirect |
| 54. C2×C4⋊C4 | D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719919 | 2 |
| C2×#11719921 | 2 |
| #13133124 | 2 |
| C2×C4⋊C4×C53 | 2 |
| #399 | 53 |