Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
478 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C22×C4 | C23×C29 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C29×#535 | C2 | semidirect |
| 3. C2×C29×#127 | C2 | semidirect |
| 4. C2×C29×#104 | C2 | semidirect |
| 5. C29×#418 | C2 | semidirect |
| 6. C2×C29×#100 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 35. C2×Q8×C29 | D4 | semidirect |
| 51. C2×D4×C29 | D4 | semidirect |
| 52. C2×D4×C29 | D4 | semidirect |
| 61. M16×C29 | D4 | semidirect |
| 64. C4⋊C4×C29 | D4 | semidirect |
| 69. C42×C29 | D4 | semidirect |
| 110. #2002 | C29 | direct (N × H) |
| 132. C2×AGL(1,ℤ/8) | C2×C29 | semidirect |
| 133. #535 | C2×C29 | semidirect |
| 134. C2×#127 | C2×C29 | semidirect |
| 135. C2×#104 | C2×C29 | semidirect |
| 136. #418 | C2×C29 | semidirect |
| 137. C2×#100 | C2×C29 | semidirect |
| 138. #339 | C2×C29 | semidirect |
| 167. C29 | #2002 | direct (N × H) |
| 174. C2×Q8 | D4×C29 | semidirect |
| 190. C2×D4 | D4×C29 | semidirect |
| 191. C2×D4 | D4×C29 | semidirect |
| 200. M16 | D4×C29 | semidirect |
| 203. C4⋊C4 | D4×C29 | semidirect |
| 208. C42 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×AGL(1,ℤ/8) | 2 |
| C29×#535 | 2 |
| C2×C29×#127 | 2 |
| C2×C29×#104 | 2 |
| C29×#418 | 2 |
| C2×C29×#100 | 2 |
| C29×#339 | 2 |
| #2002 | 29 |