Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
526 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 526 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 |
| 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. #2699×C137 | C2 | semidirect |
| 2. #2006×C137 | C2 | semidirect |
| 3. #1610×C137 | C2 | semidirect |
| 4. #1598×C137 | C2 | semidirect |
| 5. #1346×C137 | C2 | semidirect |
| 6. #1345×C137 | C2 | semidirect |
| 7. #1318×C137 | C2 | semidirect |
| 89. C2×D4×C137 | D8 | semidirect |
| 222. #12099 | C137 | direct (N × H) |
| 223. C137 | #12099 | direct (N × H) |
| 224. #2699 | C2×C137 | semidirect |
| 225. #2006 | C2×C137 | semidirect |
| 226. #1610 | C2×C137 | semidirect |
| 227. #1598 | C2×C137 | semidirect |
| 228. #1346 | C2×C137 | semidirect |
| 229. #1345 | C2×C137 | semidirect |
| 230. #1318 | C2×C137 | semidirect |
| 312. C2×D4 | D8×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2699×C137 | 2 |
| #2006×C137 | 2 |
| #1610×C137 | 2 |
| #1598×C137 | 2 |
| #1346×C137 | 2 |
| #1345×C137 | 2 |
| #1318×C137 | 2 |
| #12099 | 137 |