Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 362 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 | C2×C29 | #386 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C29×#535 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#518 | C2 | semidirect |
| 3. C29×#421 | C2 | semidirect |
| 4. C2×C29×#100 | C2 | semidirect |
| 5. C29×H(3,ℤ/4) | C2 | semidirect |
| 9. C29×#127 | C4 | semidirect |
| 10. C29×#124 | C4 | semidirect |
| 22. C2×Q8×C29 | C2×C4 | semidirect |
| 28. C2×D4×C29 | C2×C4 | semidirect |
| 42. C42×C29 | C2×C4 | semidirect |
| 43. C42×C29 | D4 | semidirect |
| 67. #1911 | C29 | direct (N × H) |
| 84. #518 | C2×C29 | semidirect |
| 85. #421 | C2×C29 | semidirect |
| 86. C2×#100 | C2×C29 | semidirect |
| 87. H(3,ℤ/4) | C2×C29 | semidirect |
| 97. #127 | C4×C29 | semidirect |
| 98. #124 | C4×C29 | semidirect |
| 107. C29 | #1911 | direct (N × H) |
| 111. C2×Q8 | C2×C4×C29 | semidirect |
| 117. C2×D4 | C2×C4×C29 | semidirect |
| 131. C42 | C2×C4×C29 | semidirect |
| 132. C42 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#535 | 2 |
| C29×#518 | 2 |
| C29×#421 | 2 |
| C2×C29×#100 | 2 |
| C29×H(3,ℤ/4) | 2 |
| #1911 | 29 |