Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
390 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C22×D4×C29 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q16×C29 | C2 | semidirect |
| 4. C2×C29×#103 | C2 | semidirect |
| 6. C29×#391 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 101. #2015 | C29 | direct (N × H) |
| 120. C22×Q16 | C2×C29 | semidirect |
| 123. C2×#103 | C2×C29 | semidirect |
| 125. #391 | C2×C29 | semidirect |
| 126. #336 | C2×C29 | semidirect |
| 152. C29 | #2015 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C29 | 2 |
| C22×SD16×C29 | 2 |
| C2×C29×#124 | 2 |
| C2×C29×#103 | 2 |
| C2×C29×#102 | 2 |
| C29×#391 | 2 |
| C29×#336 | 2 |
| #2015 | 29 |