Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
684 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 102 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×C137 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C137 |
| prime radical | #2657×C137 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3215×C137 | C2 | semidirect |
| 2. #3138×C137 | C2 | semidirect |
| 4. #1555×C137 | C2 | semidirect |
| 5. #1527×C137 | C2 | semidirect |
| 6. #1506×C137 | C2 | semidirect |
| 7. #1300×C137 | C2 | semidirect |
| 40. C4⋊Q8×C137 | D4 | semidirect |
| 41. C4⋊Q8×C137 | D4 | semidirect |
| 64. C4⋊C8×C137 | D4 | semidirect |
| 73. #97×C137 | D4 | semidirect |
| 200. #10096 | C137 | direct (N × H) |
| 201. C137 | #10096 | direct (N × H) |
| 202. #3215 | C2×C137 | semidirect |
| 203. #3138 | C2×C137 | semidirect |
| 205. #1555 | C2×C137 | semidirect |
| 206. #1527 | C2×C137 | semidirect |
| 207. #1506 | C2×C137 | semidirect |
| 208. #1300 | C2×C137 | semidirect |
| 241. C4⋊Q8 | D4×C137 | semidirect |
| 242. C4⋊Q8 | D4×C137 | semidirect |
| 265. C4⋊C8 | D4×C137 | semidirect |
| 274. #97 | D4×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3215×C137 | 2 |
| #3138×C137 | 2 |
| #2657×C137 | 2 |
| #1555×C137 | 2 |
| #1527×C137 | 2 |
| #1506×C137 | 2 |
| #1300×C137 | 2 |
| #10096 | 137 |