Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
872 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C2×#41×C61 | C4 |
| hypercenter | C2×#41 | #6923 |
| hypocenter | C61 | #2341 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×#6923 | C2 | semidirect |
| 2. #16840714 | C2 | semidirect |
| 3. #16840704 | C2 | semidirect |
| 4. C4×C22⋊#6923 | C2 | semidirect |
| 13. C2×#11758226 | C4 | semidirect |
| 14. C2×#11758222 | C4 | semidirect |
| 15. C2×#11758224 | C4 | semidirect |
| 20. C2×#41×C61 | C4 | semidirect |
| 58. C2×#6923 | #41 | semidirect |
| 59. Q8×C61 | C22⋊C4 | semidirect |
| 73. Dic122 | C22⋊C4 | semidirect |
| 106. C61 | #2341 | semidirect |
| 111. C2×#41 | #6923 | semidirect |
| 155. Q8 | C22⋊#6923 | semidirect |