Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
562 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 218 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C131 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C4×Q8×C131 ◁ C8×Q8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3391×C131 | C2 | semidirect |
| 2. Q8×D8×C131 | C2 | semidirect |
| 3. #2240×C131 | C2 | semidirect |
| 4. #2224×C131 | C2 | semidirect |
| 5. #2206×C131 | C2 | semidirect |
| 6. Q8×C16×C131 | C2 | semidirect |
| 7. C4×D16×C131 | C2 | semidirect |
| 60. D8×C131 | #41 | semidirect |
| 75. Q8×C131 | D16 | semidirect |
| 110. #33925 | C131 | direct (N × H) |
| 111. C131 | #33925 | direct (N × H) |
| 112. #3391 | C2×C131 | semidirect |
| 113. Q8×D8 | C2×C131 | semidirect |
| 114. #2240 | C2×C131 | semidirect |
| 115. #2224 | C2×C131 | semidirect |
| 116. #2206 | C2×C131 | semidirect |
| 117. Q8×C16 | C2×C131 | semidirect |
| 118. C4×D16 | C2×C131 | semidirect |
| 171. D8 | #41×C131 | semidirect |
| 186. Q8 | D16×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3391×C131 | 2 |
| Q8×D8×C131 | 2 |
| #2240×C131 | 2 |
| #2224×C131 | 2 |
| #2206×C131 | 2 |
| Q8×C16×C131 | 2 |
| C4×D16×C131 | 2 |
| #33925 | 131 |