Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C23×C29 |
| prime radical | C29×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C29 ◁ C2×Q8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#563 | C2 | semidirect |
| 2. C29×#456 | C2 | semidirect |
| 4. C29×#356 | C2 | semidirect |
| 5. C29×#355 | C2 | semidirect |
| 62. #2203 | C29 | direct (N × H) |
| 73. #563 | C2×C29 | semidirect |
| 74. #456 | C2×C29 | semidirect |
| 76. #356 | C2×C29 | semidirect |
| 77. #355 | C2×C29 | semidirect |
| 95. C29 | #2203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#563 | 2 |
| C29×#456 | 2 |
| C29×#454 | 2 |
| C29×#356 | 2 |
| C29×#355 | 2 |
| #2203 | 29 |