Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
816 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 816 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×C29 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C29 |
| prime radical | C22×#41×C29 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×C22⋊Q8 | C2 | semidirect |
| 3. C29×#395 | C2 | semidirect |
| 4. C29×#394 | C2 | semidirect |
| 5. C29×#380 | C2 | semidirect |
| 50. #2616 | C29 | direct (N × H) |
| 64. C2×C22⋊Q8 | C2×C29 | semidirect |
| 65. #395 | C2×C29 | semidirect |
| 66. #394 | C2×C29 | semidirect |
| 67. #380 | C2×C29 | semidirect |
| 83. C29 | #2616 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C29 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| C29×#395 | 2 |
| C29×#394 | 2 |
| C29×#380 | 2 |
| #2616 | 29 |