Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
848 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C2×D4 |
| commutator | C2×C4 | C22×C4×C61 |
| Frattini, cosocle | C22×C4 | C23×C61 |
| prime radical | C23×D4×C61 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C23×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#102×C61 | C2 | semidirect |
| 3. C2×C22⋊C8×C61 | C2 | semidirect |
| 4. C61×#380 | C2 | semidirect |
| 9. C22×D4×C61 | C4 | semidirect |
| 12. C22×C8×C61 | C22 | semidirect |
| 13. C2×C4⋊C4×C61 | C22 | semidirect |
| 62. D4×C61 | C22⋊C4 | semidirect |
| 84. C22×C61 | #102 | semidirect |
| 94. #1786 | C61 | direct (N × H) |
| 103. C2×#102 | C2×C61 | semidirect |
| 104. C2×C22⋊C8 | C2×C61 | semidirect |
| 105. #380 | C2×C61 | semidirect |
| 106. C61 | #1786 | direct (N × H) |
| 111. C22×D4 | C4×C61 | semidirect |
| 114. C22×C8 | C22×C61 | semidirect |
| 115. C2×C4⋊C4 | C22×C61 | semidirect |
| 164. D4 | C22⋊C4×C61 | semidirect |
| 186. C22 | #102×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C61 | 2 |
| C2×#102×C61 | 2 |
| C2×C22⋊C8×C61 | 2 |
| C61×#380 | 2 |
| #1786 | 61 |