Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
830 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 206 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ #376×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2641×C131 | C2 | semidirect |
| 2. #2054×C131 | C2 | semidirect |
| 3. #2025×C131 | C2 | semidirect |
| 4. #2011×C131 | C2 | semidirect |
| 5. #1832×C131 | C2 | semidirect |
| 90. #32814 | C131 | direct (N × H) |
| 91. C131 | #32814 | direct (N × H) |
| 92. #2641 | C2×C131 | semidirect |
| 93. #2054 | C2×C131 | semidirect |
| 94. #2025 | C2×C131 | semidirect |
| 95. #2011 | C2×C131 | semidirect |
| 96. #1832 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2641×C131 | 2 |
| #2054×C131 | 2 |
| #2025×C131 | 2 |
| #2011×C131 | 2 |
| #1832×C131 | 2 |
| #32814 | 131 |