Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
480 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 192 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×D4×C29 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#400 | C2 | semidirect |
| 2. C29×#393 | C2 | semidirect |
| 3. C29×#391 | C2 | semidirect |
| 6. C29×#385 | C2 | semidirect |
| 27. C2×D4×C29 | Q8 | semidirect |
| 65. #2804 | C29 | direct (N × H) |
| 81. #400 | C2×C29 | semidirect |
| 82. #393 | C2×C29 | semidirect |
| 83. #391 | C2×C29 | semidirect |
| 86. #385 | C2×C29 | semidirect |
| 107. C29 | #2804 | direct (N × H) |
| 114. C2×D4 | Q8×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#400 | 2 |
| C29×#393 | 2 |
| C29×#391 | 2 |
| C29×#390 | 2 |
| C29×#386 | 2 |
| C29×#385 | 2 |
| #2804 | 29 |