Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
186 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 68 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×C31 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C31 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ C4×C8×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C31×D16 | C2 | semidirect |
| 2. C31×#493 | C2 | semidirect |
| 3. C4×D8×C31 | C2 | semidirect |
| 4. C31×C4⋊C16 | C2 | semidirect |
| 5. C31×#357 | C2 | semidirect |
| 25. D8×C31 | D4 | semidirect |
| 48. #2206 | C31 | direct (N × H) |
| 58. C4×C31 | D16 | semidirect |
| 61. C2×D16 | C2×C31 | semidirect |
| 62. #493 | C2×C31 | semidirect |
| 63. C4×D8 | C2×C31 | semidirect |
| 64. C4⋊C16 | C2×C31 | semidirect |
| 65. #357 | C2×C31 | semidirect |
| 81. C31 | #2206 | direct (N × H) |
| 91. D8 | D4×C31 | semidirect |
| 123. C4 | C31×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×D16 | 2 |
| C31×#493 | 2 |
| C4×D8×C31 | 2 |
| C31×C4⋊C16 | 2 |
| C31×#357 | 2 |
| #2206 | 31 |