Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
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×D271 |
| commutator, socle, cosocle | C23×C271 | C24 |
| Fitting, prime radical | C22×#41×C271 | C2 |
| hypercenter | C22×#41 | D271 |
| hypocenter | C271 | #2432 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22576158 | C2 | semidirect |
| 2. C2×#22576147 | C2 | semidirect |
| 3. C2×#22576139 | C2 | semidirect |
| 4. #31773811 | C2 | semidirect |
| 5. #31773804 | C2 | semidirect |
| 6. #31773800 | C2 | semidirect |
| 7. #31773770 | C2 | semidirect |
| 8. C4×C22⋊Dic271 | C2 | semidirect |
| 81. C2×Dic271 | #41 | semidirect |
| 136. C271 | #2432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576158 | 2 |
| C2×#22576147 | 2 |
| C2×#22576139 | 2 |
| #31773811 | 2 |
| #31773804 | 2 |
| #31773800 | 2 |
| #31773770 | 2 |
| C4×C22⋊Dic271 | 2 |
| C22×#41×C271 | 2 |
| #2432 | 271 |