Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
288 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 104 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×C31 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C31 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 52. C2×C4×C31 | Q16 | semidirect |
| 59. #2056 | C31 | direct (N × H) |
| 93. C31 | #2056 | direct (N × H) |
| 129. C2×C4 | Q16×C31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C31 | 2 |
| C2×C31×C4⋊C8 | 2 |
| C2×C31×#103 | 2 |
| C31×#391 | 2 |
| C31×#340 | 2 |
| #2056 | 31 |