Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
476 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 74 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C4⋊C4 | C23×C137 |
| prime radical | #1598×C137 | C2 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C137 ◁ C2×C4⋊C4×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2728×C137 | C2 | semidirect |
| 2. #2007×C137 | C2 | semidirect |
| 3. #1610×C137 | C2 | semidirect |
| 5. #1346×C137 | C2 | semidirect |
| 6. #1345×C137 | C2 | semidirect |
| 7. #1319×C137 | C2 | semidirect |
| 76. C2×Q8×C137 | D8 | semidirect |
| 203. #12098 | C137 | direct (N × H) |
| 204. C137 | #12098 | direct (N × H) |
| 205. #2728 | C2×C137 | semidirect |
| 206. #2007 | C2×C137 | semidirect |
| 207. #1610 | C2×C137 | semidirect |
| 209. #1346 | C2×C137 | semidirect |
| 210. #1345 | C2×C137 | semidirect |
| 211. #1319 | C2×C137 | semidirect |
| 280. C2×Q8 | D8×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2728×C137 | 2 |
| #2007×C137 | 2 |
| #1610×C137 | 2 |
| #1598×C137 | 2 |
| #1346×C137 | 2 |
| #1345×C137 | 2 |
| #1319×C137 | 2 |
| #12098 | 137 |