Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C29 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#547 | C2 | semidirect |
| 2. C29×#486 | C2 | semidirect |
| 3. C29×#459 | C2 | semidirect |
| 4. C29×#459 | C2 | semidirect |
| 5. C29×#332 | C2 | semidirect |
| 6. C29×D4⋊C8 | C2 | semidirect |
| 7. C29×D4⋊C8 | C2 | semidirect |
| 65. D4×C29 | D8 | semidirect |
| 80. #1625 | C29 | direct (N × H) |
| 99. #547 | C2×C29 | semidirect |
| 100. #486 | C2×C29 | semidirect |
| 101. #459 | C2×C29 | semidirect |
| 102. #459 | C2×C29 | semidirect |
| 103. #332 | C2×C29 | semidirect |
| 104. D4⋊C8 | C2×C29 | semidirect |
| 105. D4⋊C8 | C2×C29 | semidirect |
| 129. C29 | #1625 | direct (N × H) |
| 170. D4 | D8×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#547 | 2 |
| C29×#486 | 2 |
| C29×#459 | 2 |
| C29×#332 | 2 |
| C29×D4⋊C8 | 2 |
| #1625 | 29 |