Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 512 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 | C24×C31 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q16×C31 | C2 | semidirect |
| 4. C31×#467 | C2 | direct (N × H) |
| 5. C2×C31×#107 | C2 | semidirect |
| 6. C2×C31×#103 | C2 | semidirect |
| 10. C2×Q16×C31 | C22 | semidirect |
| 20. C31×#107 | C22 | semidirect |
| 21. C31×#103 | C22 | semidirect |
| 47. C23×C31 | Q16 | semidirect |
| 68. C2×#467 | C31 | direct (N × H) |
| 74. C22×C31 | C2×Q16 | semidirect |
| 83. C22×Q16 | C2×C31 | semidirect |
| 86. #467 | C2×C31 | direct (N × H) |
| 87. C2×#107 | C2×C31 | semidirect |
| 88. C2×#103 | C2×C31 | semidirect |
| 90. C2×C31 | #467 | direct (N × H) |
| 97. C2×Q16 | C22×C31 | semidirect |
| 107. #107 | C22×C31 | semidirect |
| 108. #103 | C22×C31 | semidirect |
| 109. C31 | C2×#467 | direct (N × H) |
| 135. C23 | Q16×C31 | semidirect |
| 161. C22 | C2×Q16×C31 | semidirect |
| 171. C2 | C31×#467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C31 | 2 |
| C23×C8×C31 | 2 |
| C2×C31×C22⋊Q8 | 2 |
| C31×#467 | 2 |
| C2×C31×#107 | 2 |
| C2×C31×#103 | 2 |
| C2×#467 | 31 |