Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
312 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×D4 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C42 | C23×C29 |
| socle | C22×C29 | C2×C22⋊C4 |
| prime radical | C22×D4×C29 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#431 | C2 | semidirect |
| 3. C29×#423 | C2 | semidirect |
| 4. C29×D4⋊C8 | C2 | semidirect |
| 17. C29×C4⋊C8 | C22 | semidirect |
| 19. C4×C8×C29 | C22 | semidirect |
| 50. D4×C29 | M16 | semidirect |
| 68. #1486 | C29 | direct (N × H) |
| 86. #431 | C2×C29 | semidirect |
| 87. #423 | C2×C29 | semidirect |
| 88. D4⋊C8 | C2×C29 | semidirect |
| 106. C4⋊C8 | C22×C29 | semidirect |
| 108. C4×C8 | C22×C29 | semidirect |
| 109. C29 | #1486 | direct (N × H) |
| 140. D4 | M16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C29 | 2 |
| C29×#431 | 2 |
| C29×#423 | 2 |
| C29×D4⋊C8 | 2 |
| #1486 | 29 |