Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
232 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 232 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 | C2×C71 | #2085 |
| commutator, Frattini, cosocle | C22×C8 | C23×C71 |
| prime radical | C23×C71 | #135 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C22×C4×C71 ◁ #405×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 102. #13512 | C71 | direct (N × H) |
| 114. C71 | #13512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2161 | 2 |
| C71×#2155 | 2 |
| C71×#1951 | 2 |
| C71×#1833 | 2 |
| C71×#1386 | 2 |
| C71×#1383 | 2 |
| C71×#1378 | 2 |
| #13512 | 71 |