Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
246 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C71 | C42 |
| commutator | C4 | C4×C16×C71 |
| Frattini, cosocle | C2×C4×C8 | C22×C71 |
| socle | C22×C71 | #336 |
| prime radical | C23×C71 | C22⋊C8 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C4×C16×C71 | C4 | semidirect |
| 34. C42×C71 | C16 | semidirect |
| 69. #7142 | C71 | direct (N × H) |
| 76. C71 | #7142 | direct (N × H) |
| 82. C4×C16 | C4×C71 | semidirect |
| 108. C42 | C16×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2162 | 2 |
| C71×#1744 | 2 |
| #7142 | 71 |