Finite Group DatabasebetaFinite Group DatabasebetaOrder 38656.
650 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 122 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×C151 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C151 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×C8×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#509×C151 | C2 | semidirect |
| 2. C2×#493×C151 | C2 | semidirect |
| 3. C2×#361×C151 | C2 | semidirect |
| 4. #1974×C151 | C2 | semidirect |
| 5. #1376×C151 | C2 | semidirect |
| 26. C2×Q16×C151 | D4 | semidirect |
| 37. C2×D8×C151 | D4 | semidirect |
| 47. M32×C151 | D4 | semidirect |
| 147. #13331 | C151 | direct (N × H) |
| 148. C151 | #13331 | direct (N × H) |
| 149. C2×#509 | C2×C151 | semidirect |
| 150. C2×#493 | C2×C151 | semidirect |
| 151. C2×#361 | C2×C151 | semidirect |
| 152. #1974 | C2×C151 | semidirect |
| 153. #1376 | C2×C151 | semidirect |
| 174. C2×Q16 | D4×C151 | semidirect |
| 185. C2×D8 | D4×C151 | semidirect |
| 195. M32 | D4×C151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#509×C151 | 2 |
| C2×#493×C151 | 2 |
| C2×#361×C151 | 2 |
| #1974×C151 | 2 |
| #1376×C151 | 2 |
| #13331 | 151 |