Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
272 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 168 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 | C4 | C2×C42×C31 |
| Frattini, cosocle | C22×C4 | C23×C31 |
| LCS | G ▷ 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 |
|---|---|---|
| 12. C31×#107 | C4 | semidirect |
| 13. C31×#106 | C4 | semidirect |
| 14. C31×#97 | C4 | semidirect |
| 50. C8×C31 | C42 | semidirect |
| 51. #1776 | C31 | direct (N × H) |
| 80. #107 | C4×C31 | semidirect |
| 81. #106 | C4×C31 | semidirect |
| 82. #97 | C4×C31 | semidirect |
| 84. C31 | #1776 | direct (N × H) |
| 119. C8 | C42×C31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×#107 | 2 |
| C2×C31×#106 | 2 |
| C2×C31×#97 | 2 |
| C4×C4⋊C4×C31 | 2 |
| C31×#340 | 2 |
| #1776 | 31 |