Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C29 |
| socle | C22×C29 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#135 | C2 | semidirect |
| 2. C29×#532 | C2 | semidirect |
| 3. C29×#497 | C2 | semidirect |
| 4. C29×#496 | C2 | semidirect |
| 5. C2×C29×#97 | C2 | semidirect |
| 30. C2×C8×C29 | D4 | semidirect |
| 50. #3150 | C29 | direct (N × H) |
| 60. C2×#135 | C2×C29 | semidirect |
| 61. #532 | C2×C29 | semidirect |
| 62. #497 | C2×C29 | semidirect |
| 63. #496 | C2×C29 | semidirect |
| 64. C2×#97 | C2×C29 | semidirect |
| 82. C29 | #3150 | direct (N × H) |
| 94. C2×C8 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#135 | 2 |
| C29×#532 | 2 |
| C29×#497 | 2 |
| C29×#496 | 2 |
| C2×C29×#97 | 2 |
| #3150 | 29 |