Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C29 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#509 | C2 | semidirect |
| 2. C29×#493 | C2 | semidirect |
| 3. C29×#443 | C2 | semidirect |
| 4. C29×#364 | C2 | semidirect |
| 5. C29×#361 | C2 | semidirect |
| 20. Q16×C29 | D4 | semidirect |
| 26. D8×C29 | D4 | semidirect |
| 49. #2213 | C29 | direct (N × H) |
| 58. #509 | C2×C29 | semidirect |
| 59. #493 | C2×C29 | semidirect |
| 60. #443 | C2×C29 | semidirect |
| 61. #364 | C2×C29 | semidirect |
| 62. #361 | C2×C29 | semidirect |
| 78. C29 | #2213 | direct (N × H) |
| 82. Q16 | D4×C29 | semidirect |
| 88. D8 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#509 | 2 |
| C29×#493 | 2 |
| C29×#443 | 2 |
| C29×#364 | 2 |
| C29×#361 | 2 |
| #2213 | 29 |