Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
386 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C137 |
| prime radical | #532×C137 | C22 |
| 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 |
|---|---|---|
| 2. #1843×C137 | C2 | semidirect |
| 3. #1552×C137 | C2 | semidirect |
| 5. #1506×C137 | C2 | semidirect |
| 7. #1290×C137 | C2 | semidirect |
| 157. #10514 | C137 | direct (N × H) |
| 158. C137 | #10514 | direct (N × H) |
| 160. #1843 | C2×C137 | semidirect |
| 161. #1552 | C2×C137 | semidirect |
| 163. #1506 | C2×C137 | semidirect |
| 165. #1290 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3246×C137 | 2 |
| #1843×C137 | 2 |
| #1552×C137 | 2 |
| #1551×C137 | 2 |
| #1506×C137 | 2 |
| #1505×C137 | 2 |
| #1290×C137 | 2 |
| #10514 | 137 |