Finite Group DatabasebetaFinite Group DatabasebetaOrder 8384.
234 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 106 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×C131 | C23 |
| commutator | C22 | C22×C4×C131 |
| Frattini, cosocle | C23 | C23×C131 |
| prime radical | C24×C131 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊C4×C131 | C2 | semidirect |
| 5. #95×C131 | C2 | semidirect |
| 15. C22⋊C4×C131 | C4 | semidirect |
| 31. C2×C4×C131 | C2×C4 | semidirect |
| 37. C22×C131 | C4⋊C4 | semidirect |
| 53. C131 | #385 | direct (N × H) |
| 54. #385 | C131 | direct (N × H) |
| 56. C2×C4⋊C4 | C2×C131 | semidirect |
| 59. #95 | C2×C131 | semidirect |
| 69. C22⋊C4 | C4×C131 | semidirect |
| 85. C2×C4 | C2×C4×C131 | semidirect |
| 91. C22 | C4⋊C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C131 | 2 |
| C2×C4⋊C4×C131 | 2 |
| C2×C22⋊C4×C131 | 2 |
| #95×C131 | 2 |
| #385 | 131 |