Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
914 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C2×#95×C271 | C2 |
| hypercenter | C2×#95 | D271 |
| hypocenter | C271 | #2430 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#16864654 | C2 | semidirect |
| 2. C2×#22576143 | C2 | semidirect |
| 3. C2×#22576134 | C2 | semidirect |
| 4. #31773818 | C2 | semidirect |
| 5. #31773815 | C2 | semidirect |
| 6. #31773810 | C2 | semidirect |
| 7. #31773807 | C2 | semidirect |
| 8. #31773776 | C2 | semidirect |
| 9. #31773775 | C2 | semidirect |
| 10. #31773771 | C2 | semidirect |
| 11. C2×#95×C271 | C2 | semidirect |
| 53. C2×C22⋊D271 | D4 | semidirect |
| 76. C22×C4×C271 | D4 | semidirect |
| 126. C2×C4×C271 | #41 | semidirect |
| 165. C271 | #2430 | semidirect |
| 177. C2×#95 | D271 | semidirect |
| 232. C22×C4 | D1084 | semidirect |
| 292. C2×C4 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C2×#22576143 | 2 |
| C2×#22576134 | 2 |
| #31773818 | 2 |
| #31773815 | 2 |
| #31773810 | 2 |
| #31773807 | 2 |
| #31773776 | 2 |
| #31773775 | 2 |
| #31773771 | 2 |
| C2×#95×C271 | 2 |
| #2430 | 271 |