Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1008 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 242 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 | C23×C4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C23×C4 | #6923 |
| hypocenter | C61 | C2×#407 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11758213 | C2 | semidirect |
| 2. #16840733 | C2 | direct (N × H) |
| 3. C2×#14519834 | C2 | semidirect |
| 4. C2×C22⋊#92420 | C2 | semidirect |
| 7. C2×#11758213 | C22 | semidirect |
| 8. C22×#92420 | C22 | semidirect |
| 9. #14519834 | C22 | semidirect |
| 10. C22⋊#92420 | C22 | semidirect |
| 50. C2×#92420 | C23 | semidirect |
| 54. C23×C61 | M16 | semidirect |
| 66. C22×D61 | M16 | semidirect |
| 94. C22×C61 | C2×M16 | semidirect |
| 104. C2×D61 | C2×M16 | semidirect |
| 112. C2×C61 | #407 | semidirect |
| 123. C61 | C2×#407 | semidirect |
| 184. C23 | #11758213 | semidirect |
| 221. C22 | C2×#11758213 | semidirect |
| 231. C2 | #16840733 | direct (N × H) |