Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
240 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 86 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×C131 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | #493×C131 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ C82×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2225×C131 | C2 | semidirect |
| 4. C8×Q16×C131 | C2 | semidirect |
| 5. #1367×C131 | C2 | semidirect |
| 6. #1364×C131 | C2 | semidirect |
| 51. Q16×C131 | SD16 | semidirect |
| 91. C8×C131 | SD32 | semidirect |
| 110. #12417 | C131 | direct (N × H) |
| 111. C131 | #12417 | direct (N × H) |
| 112. #2225 | C2×C131 | semidirect |
| 115. C8×Q16 | C2×C131 | semidirect |
| 116. #1367 | C2×C131 | semidirect |
| 117. #1364 | C2×C131 | semidirect |
| 162. Q16 | SD16×C131 | semidirect |
| 202. C8 | SD32×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2225×C131 | 2 |
| #2207×C131 | 2 |
| #1706×C131 | 2 |
| C8×Q16×C131 | 2 |
| #1367×C131 | 2 |
| #1364×C131 | 2 |
| #1361×C131 | 2 |
| #12417 | 131 |