Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
154 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 68 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×C37 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C37 |
| prime radical | C2×D4×C37 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37×#500 | C2 | semidirect |
| 4. C37×#334 | C2 | semidirect |
| 5. C37×#333 | C2 | semidirect |
| 54. #1695 | C37 | direct (N × H) |
| 59. #500 | C2×C37 | semidirect |
| 62. #334 | C2×C37 | semidirect |
| 63. #333 | C2×C37 | semidirect |
| 64. C37 | #1695 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#500 | 2 |
| C37×#476 | 2 |
| C37×#436 | 2 |
| C37×#334 | 2 |
| C37×#333 | 2 |
| #1695 | 37 |