Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
332 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C2×D4 |
| commutator | C2×C4 | C22×C4×C61 |
| Frattini, cosocle | C22×C4 | C23×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C4⋊Q8×C61 | C4 | semidirect |
| 54. C4×C61 | #103 | semidirect |
| 57. #1956 | C61 | direct (N × H) |
| 67. C61 | #1956 | direct (N × H) |
| 71. C4⋊Q8 | C4×C61 | semidirect |
| 117. C4 | #103×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Q8×C61 | 2 |
| C2×#103×C61 | 2 |
| C2×C4×C8×C61 | 2 |
| C61×#384 | 2 |
| #1956 | 61 |