Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
212 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 96 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×C131 | #121 |
| commutator | C2×C4 | C22×C4×C131 |
| Frattini, cosocle | C22×C4 | C23×C131 |
| prime radical | C23×C131 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. #101×C131 | C4 | semidirect |
| 93. C131 | #1930 | direct (N × H) |
| 94. #1930 | C131 | direct (N × H) |
| 115. #101 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #428×C131 | 2 |
| #419×C131 | 2 |
| C2×#103×C131 | 2 |
| C2×#101×C131 | 2 |
| #405×C131 | 2 |
| #343×C131 | 2 |
| #341×C131 | 2 |
| #1930 | 131 |