Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
368 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C137 |
| prime radical | #3277×C137 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C42×C137 ◁ #436×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2251×C137 | C2 | semidirect |
| 3. #2209×C137 | C2 | semidirect |
| 4. #1689×C137 | C2 | semidirect |
| 5. #1360×C137 | C2 | semidirect |
| 6. #1334×C137 | C2 | semidirect |
| 7. #1330×C137 | C2 | semidirect |
| 165. #12327 | C137 | direct (N × H) |
| 166. C137 | #12327 | direct (N × H) |
| 168. #2251 | C2×C137 | semidirect |
| 169. #2209 | C2×C137 | semidirect |
| 170. #1689 | C2×C137 | semidirect |
| 171. #1360 | C2×C137 | semidirect |
| 172. #1334 | C2×C137 | semidirect |
| 173. #1330 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3277×C137 | 2 |
| #2251×C137 | 2 |
| #2209×C137 | 2 |
| #1689×C137 | 2 |
| #1360×C137 | 2 |
| #1334×C137 | 2 |
| #1330×C137 | 2 |
| #12327 | 137 |