Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
416 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C61 |
| prime radical | C24×C61 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C61×#484 | C2 | semidirect |
| 3. C61×#467 | C2 | semidirect |
| 4. C61×#451 | C2 | semidirect |
| 8. C2×Q16×C61 | C22 | semidirect |
| 17. #107×C61 | C22 | semidirect |
| 18. #103×C61 | C22 | semidirect |
| 42. C23×C61 | Q16 | semidirect |
| 72. #3189 | C61 | direct (N × H) |
| 79. #484 | C2×C61 | semidirect |
| 80. #467 | C2×C61 | semidirect |
| 81. #451 | C2×C61 | semidirect |
| 83. C61 | #3189 | direct (N × H) |
| 86. C2×Q16 | C22×C61 | semidirect |
| 95. #107 | C22×C61 | semidirect |
| 96. #103 | C22×C61 | semidirect |
| 120. C23 | Q16×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8×C61 | 2 |
| C61×#484 | 2 |
| C61×#467 | 2 |
| C61×#451 | 2 |
| C2×C22⋊C8×C61 | 2 |
| #3189 | 61 |