Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
1034 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C22×C4 | C22×C4×C137 |
| Frattini, cosocle | C23×C4 | C23×C137 |
| prime radical | #2433×C137 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2308×C137 | C2 | semidirect |
| 3. #1783×C137 | C2 | semidirect |
| 4. #1510×C137 | C2 | semidirect |
| 5. #1284×C137 | C2 | semidirect |
| 7. C2×#127×C137 | C4 | semidirect |
| 15. #390×C137 | C4 | semidirect |
| 30. C22×D4×C137 | C2×C4 | semidirect |
| 40. C2×C4⋊C4×C137 | C2×C4 | semidirect |
| 50. C2×C42×C137 | C2×C4 | semidirect |
| 56. #95×C137 | D4 | semidirect |
| 220. #9463 | C137 | direct (N × H) |
| 221. C137 | #9463 | direct (N × H) |
| 223. #2308 | C2×C137 | semidirect |
| 224. #1783 | C2×C137 | semidirect |
| 225. #1510 | C2×C137 | semidirect |
| 226. #1284 | C2×C137 | semidirect |
| 228. C2×#127 | C4×C137 | semidirect |
| 236. #390 | C4×C137 | semidirect |
| 251. C22×D4 | C2×C4×C137 | semidirect |
| 261. C2×C4⋊C4 | C2×C4×C137 | semidirect |
| 271. C2×C42 | C2×C4×C137 | semidirect |
| 277. #95 | D4×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2433×C137 | 2 |
| #2308×C137 | 2 |
| #1783×C137 | 2 |
| #1510×C137 | 2 |
| #1284×C137 | 2 |
| #9463 | 137 |