Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
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×C37 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C4×C8×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37×#509 | C2 | semidirect |
| 2. C37×#493 | C2 | semidirect |
| 3. C37×#443 | C2 | semidirect |
| 4. C37×#364 | C2 | semidirect |
| 5. C37×#361 | C2 | semidirect |
| 20. Q16×C37 | D4 | semidirect |
| 26. D8×C37 | D4 | semidirect |
| 57. #2213 | C37 | direct (N × H) |
| 62. #509 | C2×C37 | semidirect |
| 63. #493 | C2×C37 | semidirect |
| 64. #443 | C2×C37 | semidirect |
| 65. #364 | C2×C37 | semidirect |
| 66. #361 | C2×C37 | semidirect |
| 67. C37 | #2213 | direct (N × H) |
| 82. Q16 | D4×C37 | semidirect |
| 88. D8 | D4×C37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#509 | 2 |
| C37×#493 | 2 |
| C37×#443 | 2 |
| C37×#364 | 2 |
| C37×#361 | 2 |
| #2213 | 37 |