Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1360 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#6923 |
| commutator | C22×C61 | C23×C4 |
| Frattini | C22 | C23×#6923 |
| Fitting | C22×D4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C22×D4 | #6923 |
| hypocenter | C61 | C2×#390 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊#6923 | C2 | semidirect |
| 2. C22×C22⋊#6923 | C2 | semidirect |
| 3. C22×C4×#6923 | C2 | semidirect |
| 4. #16840714 | C2 | direct (N × H) |
| 9. C2×C4⋊#6923 | C22 | semidirect |
| 11. C2×C22⋊#6923 | C22 | semidirect |
| 13. C2×C4×#6923 | C22 | semidirect |
| 15. C22×D244 | C4 | semidirect |
| 16. C22×C22⋊D61 | C4 | semidirect |
| 19. C2×D4×D61 | C4 | semidirect |
| 22. C22×D4×C61 | C4 | semidirect |
| 36. C22×#6923 | D4 | semidirect |
| 40. C2×D4×C61 | C2×C4 | semidirect |
| 43. C2×C22⋊D61 | C2×C4 | semidirect |
| 49. C2×D244 | C2×C4 | semidirect |
| 85. C2×#6923 | C2×D4 | semidirect |
| 87. C2×C4×C61 | C22⋊C4 | semidirect |
| 90. C2×Dic61 | C22⋊C4 | semidirect |
| 93. C4×D61 | C22⋊C4 | semidirect |
| 120. C4×C61 | C2×C22⋊C4 | semidirect |
| 121. Dic61 | C2×C22⋊C4 | semidirect |
| 124. C2×C61 | #390 | semidirect |
| 128. D61 | #390 | semidirect |
| 137. C61 | C2×#390 | semidirect |
| 145. C22×D4 | #6923 | semidirect |
| 172. C2×D4 | C2×#6923 | semidirect |
| 226. C2×C4 | C22⋊#6923 | semidirect |
| 253. C4 | C2×C22⋊#6923 | semidirect |
| 260. C2 | #16840714 | direct (N × H) |