Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
162 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | C2×D4 |
| commutator | C2×C4 | C22×C4×C31 |
| Frattini, cosocle | C42 | C23×C31 |
| socle | C22×C31 | C4×D4 |
| prime radical | C2×D4×C31 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C4×C8×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#446 | C2 | semidirect |
| 4. C31×#335 | C2 | semidirect |
| 5. C31×Q8⋊C8 | C2 | semidirect |
| 7. C31×#322 | C2 | semidirect |
| 60. C8×C31 | M16 | semidirect |
| 61. #1592 | C31 | direct (N × H) |
| 74. #446 | C2×C31 | semidirect |
| 77. #335 | C2×C31 | semidirect |
| 78. Q8⋊C8 | C2×C31 | semidirect |
| 80. #322 | C2×C31 | semidirect |
| 100. C31 | #1592 | direct (N × H) |
| 138. C8 | M16×C31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#446 | 2 |
| C4×SD16×C31 | 2 |
| C31×#436 | 2 |
| C31×#335 | 2 |
| C31×Q8⋊C8 | 2 |
| C31×D4⋊C8 | 2 |
| C31×#322 | 2 |
| #1592 | 31 |