Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
528 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C137 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C22×C4×C137 ◁ C2×C22⋊C8×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3186×C137 | C2 | semidirect |
| 2. #2184×C137 | C2 | semidirect |
| 3. #1999×C137 | C2 | semidirect |
| 4. #1347×C137 | C2 | semidirect |
| 5. #1314×C137 | C2 | semidirect |
| 6. C22×D8×C137 | C22 | semidirect |
| 17. C22⋊C16×C137 | C22 | semidirect |
| 18. #340×C137 | C22 | semidirect |
| 27. C2×D8×C137 | D4 | semidirect |
| 43. #107×C137 | D4 | semidirect |
| 107. C23×C137 | D16 | semidirect |
| 171. #12102 | C137 | direct (N × H) |
| 172. C137 | #12102 | direct (N × H) |
| 173. #3186 | C2×C137 | semidirect |
| 174. #2184 | C2×C137 | semidirect |
| 175. #1999 | C2×C137 | semidirect |
| 176. #1347 | C2×C137 | semidirect |
| 177. #1314 | C2×C137 | semidirect |
| 178. C22×D8 | C22×C137 | semidirect |
| 189. C22⋊C16 | C22×C137 | semidirect |
| 190. #340 | C22×C137 | semidirect |
| 199. C2×D8 | D4×C137 | semidirect |
| 215. #107 | D4×C137 | semidirect |
| 279. C23 | D16×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3186×C137 | 2 |
| #2184×C137 | 2 |
| #1999×C137 | 2 |
| #1347×C137 | 2 |
| #1314×C137 | 2 |
| #12102 | 137 |