Finite Group DatabasebetaFinite Group DatabasebetaOrder 38656.
246 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #442 |
| commutator | C8 | C22×C8×C151 |
| Frattini, cosocle | C4×C8 | C23×C151 |
| prime radical | C2×D16×C151 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C42×C151 ◁ #322×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1580×C151 | C2 | semidirect |
| 3. #1368×C151 | C2 | semidirect |
| 4. #1333×C151 | C2 | semidirect |
| 5. #1313×C151 | C2 | semidirect |
| 19. D16×C151 | C8 | semidirect |
| 32. D8×C151 | C2×C8 | semidirect |
| 43. C16×C151 | C2×C8 | semidirect |
| 68. #12067 | C151 | direct (N × H) |
| 69. C151 | #12067 | direct (N × H) |
| 71. #1580 | C2×C151 | semidirect |
| 72. #1368 | C2×C151 | semidirect |
| 73. #1333 | C2×C151 | semidirect |
| 74. #1313 | C2×C151 | semidirect |
| 88. D16 | C8×C151 | semidirect |
| 101. D8 | C2×C8×C151 | semidirect |
| 112. C16 | C2×C8×C151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2177×C151 | 2 |
| #1580×C151 | 2 |
| #1368×C151 | 2 |
| #1333×C151 | 2 |
| #1313×C151 | 2 |
| #12067 | 151 |