Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
830 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C24 |
| commutator | C23 | C23×C4×C71 |
| Frattini, cosocle | C22×C4 | C24×C71 |
| socle | C23×C71 | C23×C4 |
| prime radical | C24×C71 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C71×#1840 | C2 | semidirect |
| 46. #20773 | C71 | direct (N × H) |
| 51. #1840 | C2×C71 | semidirect |
| 53. C71 | #20773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#376×C71 | 2 |
| C71×#1840 | 2 |
| C71×#1728 | 2 |
| #20773 | 71 |