Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
882 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C131 |
| prime radical | C2×#127×C131 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#564×C131 | C2 | semidirect |
| 3. #1658×C131 | C2 | direct (N × H) |
| 4. C2×#330×C131 | C2 | semidirect |
| 6. #564×C131 | C22 | semidirect |
| 14. #330×C131 | C22 | semidirect |
| 67. C2×C131 | #1658 | direct (N × H) |
| 69. C2×#1658 | C131 | direct (N × H) |
| 70. C131 | C2×#1658 | direct (N × H) |
| 71. C2×#564 | C2×C131 | semidirect |
| 73. #1658 | C2×C131 | direct (N × H) |
| 74. C2×#330 | C2×C131 | semidirect |
| 76. #564 | C22×C131 | semidirect |
| 84. #330 | C22×C131 | semidirect |
| 137. C2 | #1658×C131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#564×C131 | 2 |
| C2×#490×C131 | 2 |
| #1658×C131 | 2 |
| C2×#330×C131 | 2 |
| C2×#1658 | 131 |