Finite Group DatabasebetaFinite Group DatabasebetaOrder 38656.
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 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×C151 | #2215 |
| commutator, Frattini, cosocle | C2×C16 | C23×C151 |
| prime radical | #41×C151 | D8 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C2×C4×C151 ◁ #131×C151 ◁ #504×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q64×C151 | C2 | semidirect |
| 4. #1425×C151 | C2 | semidirect |
| 5. #1420×C151 | C2 | semidirect |
| 66. #13701 | C151 | direct (N × H) |
| 67. C151 | #13701 | direct (N × H) |
| 68. C2×Q64 | C2×C151 | semidirect |
| 71. #1425 | C2×C151 | semidirect |
| 72. #1420 | C2×C151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q64×C151 | 2 |
| #2258×C151 | 2 |
| #2222×C151 | 2 |
| #1425×C151 | 2 |
| #1420×C151 | 2 |
| #13701 | 151 |