Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
924 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 288 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C31×#127 | C2 | semidirect |
| 2. C2×C31×#121 | C2 | semidirect |
| 3. C22×C42×C31 | C2 | semidirect |
| 4. C31×#390 | C2 | semidirect |
| 5. C31×#384 | C2 | semidirect |
| 24. C22×C4×C31 | D4 | semidirect |
| 31. C42×C31 | D4 | semidirect |
| 49. #2856 | C31 | direct (N × H) |
| 55. C22×C31 | #127 | semidirect |
| 61. C4×C31 | #121 | semidirect |
| 62. C2×#127 | C2×C31 | semidirect |
| 63. C2×#121 | C2×C31 | semidirect |
| 64. C22×C42 | C2×C31 | semidirect |
| 65. #390 | C2×C31 | semidirect |
| 66. #384 | C2×C31 | semidirect |
| 82. C31 | #2856 | direct (N × H) |
| 91. C22×C4 | D4×C31 | semidirect |
| 98. C42 | D4×C31 | semidirect |
| 121. C22 | C31×#127 | semidirect |
| 127. C4 | C31×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×#127 | 2 |
| C2×C31×#121 | 2 |
| C22×C42×C31 | 2 |
| C31×#390 | 2 |
| C31×#384 | 2 |
| #2856 | 31 |