Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
1382 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 298 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 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C137 |
| prime radical | C2×H(5,𝔽2)×C137 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ 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. #2487×C137 | C2 | semidirect |
| 3. #1867×C137 | C2 | semidirect |
| 4. #1799×C137 | C2 | semidirect |
| 13. C22×C4⋊C4×C137 | C22 | semidirect |
| 19. #385×C137 | C22 | semidirect |
| 21. #380×C137 | C22 | semidirect |
| 22. #342×C137 | C22 | semidirect |
| 170. #32976 | C137 | direct (N × H) |
| 171. C137 | #32976 | direct (N × H) |
| 173. #2487 | C2×C137 | semidirect |
| 174. #1867 | C2×C137 | semidirect |
| 175. #1799 | C2×C137 | semidirect |
| 184. C22×C4⋊C4 | C22×C137 | semidirect |
| 190. #385 | C22×C137 | semidirect |
| 192. #380 | C22×C137 | semidirect |
| 193. #342 | C22×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×H(5,𝔽2)×C137 | 2 |
| #2487×C137 | 2 |
| #1867×C137 | 2 |
| #1799×C137 | 2 |
| #1790×C137 | 2 |
| #32976 | 137 |