Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
436 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C137 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C137 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 109. C4⋊C4×C137 | Q16 | semidirect |
| 184. #7761 | C137 | direct (N × H) |
| 185. C137 | #7761 | direct (N × H) |
| 294. C4⋊C4 | Q16×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2806×C137 | 2 |
| #2058×C137 | 2 |
| #2024×C137 | 2 |
| #2016×C137 | 2 |
| #1272×C137 | 2 |
| #1271×C137 | 2 |
| #7761 | 137 |