Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
270 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 270 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 | C4×C71 | #410 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C2×M16 | C23×C71 |
| socle | C2×C71 | #1467 |
| prime radical | C23×C71 | C2×M16 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C71 ◁ C2×C8×C71 ◁ #405×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 88. #11539 | C71 | direct (N × H) |
| 96. C71 | #11539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2960 | 2 |
| C71×#2166 | 2 |
| C71×#1328 | 2 |
| C71×#1327 | 2 |
| #11539 | 71 |