Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
164 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C22×C8 |
| Fitting | C4×D4×C61 | C4 |
| hypercenter | C4×D4 | #6923 |
| hypocenter | C61 | #2168 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519851 | C2 | semidirect |
| 2. C22×#11758187 | C2 | semidirect |
| 3. C4⋊#11758187 | C2 | semidirect |
| 4. C22⋊#11758187 | C2 | semidirect |
| 5. C22⋊#11758187 | C2 | semidirect |
| 6. #16840650 | C2 | semidirect |
| 39. #11758187 | D4 | semidirect |
| 62. C22×C61 | M32 | semidirect |
| 83. C61 | #2168 | semidirect |
| 138. C22 | #14519851 | semidirect |