Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
322 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | #1613 |
| commutator, Frattini, cosocle | C2×M16 | C23×C137 |
| prime radical | #3204×C137 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ C2×C4×C137 ◁ C2×M16×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2239×C137 | C2 | semidirect |
| 3. #2238×C137 | C2 | semidirect |
| 4. #2098×C137 | C2 | semidirect |
| 5. #1340×C137 | C2 | semidirect |
| 6. #1339×C137 | C2 | semidirect |
| 7. #1321×C137 | C2 | semidirect |
| 153. #12303 | C137 | direct (N × H) |
| 154. C137 | #12303 | direct (N × H) |
| 156. #2239 | C2×C137 | semidirect |
| 157. #2238 | C2×C137 | semidirect |
| 158. #2098 | C2×C137 | semidirect |
| 159. #1340 | C2×C137 | semidirect |
| 160. #1339 | C2×C137 | semidirect |
| 161. #1321 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3204×C137 | 2 |
| #2239×C137 | 2 |
| #2238×C137 | 2 |
| #2098×C137 | 2 |
| #1340×C137 | 2 |
| #1339×C137 | 2 |
| #1321×C137 | 2 |
| #12303 | 137 |