Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
528 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 232 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×C31 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C31 |
| prime radical | C2×C31×#127 | C2 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 1. C2×C31×C4⋊Q8 | C2 | semidirect |
| 3. C31×#486 | C2 | direct (N × H) |
| 4. C2×C31×#102 | C2 | semidirect |
| 5. C2×C4×C8×C31 | C2 | semidirect |
| 12. C31×C4⋊Q8 | C22 | semidirect |
| 18. C31×#102 | C22 | semidirect |
| 19. C4×C8×C31 | C22 | semidirect |
| 61. C2×#486 | C31 | direct (N × H) |
| 75. C2×C4⋊Q8 | C2×C31 | semidirect |
| 77. #486 | C2×C31 | direct (N × H) |
| 78. C2×#102 | C2×C31 | semidirect |
| 79. C2×C4×C8 | C2×C31 | semidirect |
| 81. C2×C31 | #486 | direct (N × H) |
| 91. C4⋊Q8 | C22×C31 | semidirect |
| 97. #102 | C22×C31 | semidirect |
| 98. C4×C8 | C22×C31 | semidirect |
| 99. C31 | C2×#486 | direct (N × H) |
| 155. C2 | C31×#486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×C4⋊Q8 | 2 |
| C2×C31×#127 | 2 |
| C31×#486 | 2 |
| C2×C31×#102 | 2 |
| C2×C4×C8×C31 | 2 |
| C2×#486 | 31 |