Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
380 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 98 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. #1848×C137 | C2 | semidirect |
| 3. #1561×C137 | C2 | semidirect |
| 5. #1493×C137 | C2 | semidirect |
| 7. #1309×C137 | C2 | semidirect |
| 164. #10532 | C137 | direct (N × H) |
| 165. C137 | #10532 | direct (N × H) |
| 167. #1848 | C2×C137 | semidirect |
| 168. #1561 | C2×C137 | semidirect |
| 170. #1493 | C2×C137 | semidirect |
| 172. #1309 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3254×C137 | 2 |
| #1848×C137 | 2 |
| #1561×C137 | 2 |
| #1560×C137 | 2 |
| #1493×C137 | 2 |
| #1492×C137 | 2 |
| #1309×C137 | 2 |
| #10532 | 137 |