Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
696 conjugacy classes of subgroups; only the 520 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 520 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×C29 | C24 |
| commutator | C2 | C22×C42×C29 |
| Frattini, cosocle | C23 | C24×C29 |
| prime radical | C24×C29 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C4⋊C4×C29 | C2 | semidirect |
| 7. C29×#117 | C4 | semidirect |
| 8. C2×C4⋊C4×C29 | C4 | semidirect |
| 24. C4⋊C4×C29 | C2×C4 | semidirect |
| 27. C42×C29 | C2×C4 | semidirect |
| 37. C2×C4×C29 | C42 | semidirect |
| 43. #2274 | C29 | direct (N × H) |
| 57. C4×C4⋊C4 | C2×C29 | semidirect |
| 66. #117 | C4×C29 | semidirect |
| 67. C2×C4⋊C4 | C4×C29 | semidirect |
| 74. C29 | #2274 | direct (N × H) |
| 84. C4⋊C4 | C2×C4×C29 | semidirect |
| 87. C42 | C2×C4×C29 | semidirect |
| 97. C2×C4 | C42×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#117 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C4×C4⋊C4×C29 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #2274 | 29 |