Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1116 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 197 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×D157 |
| commutator, socle, cosocle | C23×C157 | C24 |
| Fitting, prime radical | C23×D4×C157 | C2 |
| hypercenter | C23×D4 | D157 |
| hypocenter | C157 | #2405 |
| LCS | G ▷ C23×C157 ▷ C157 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19097752 | C2 | semidirect |
| 2. C22×C22⋊Dic157 | C2 | semidirect |
| 3. #23757187 | C2 | semidirect |
| 4. #23757153 | C2 | semidirect |
| 5. #23757146 | C2 | semidirect |
| 6. #23757129 | C2 | semidirect |
| 7. #23757129 | C2 | semidirect |
| 9. C23×Dic157 | C22 | semidirect |
| 10. C23×Dic157 | C22 | semidirect |
| 12. C2×#14578933 | C22 | semidirect |
| 16. C2×C22⋊Dic157 | C22 | semidirect |
| 17. C2×C22⋊Dic157 | C22 | semidirect |
| 18. C2×C22⋊Dic157 | C22 | semidirect |
| 19. C2×C22⋊Dic157 | C22 | semidirect |
| 20. C2×C22⋊Dic157 | C22 | semidirect |
| 21. #19097678 | C22 | semidirect |
| 125. C22×C157 | #123 | semidirect |
| 142. C157 | #2405 | semidirect |
| 268. C22 | #19097752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097752 | 2 |
| C22×C22⋊Dic157 | 2 |
| #23757187 | 2 |
| #23757153 | 2 |
| #23757146 | 2 |
| #23757129 | 2 |
| C23×D4×C157 | 2 |
| #2405 | 157 |