Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1422 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 555 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D71 |
| commutator | C23×C71 | C23×C4 |
| Fitting | C2×C43×C71 | C2 |
| socle, prime radical, cosocle | C24×C71 | C24 |
| hypercenter | C2×C43 | D71 |
| hypocenter | C71 | #14688 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C2×C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C43×C71 | C4 | semidirect |
| 45. C42×C71 | C4⋊C4 | semidirect |
| 74. C4×C71 | #383 | semidirect |
| 86. C71 | #14688 | semidirect |
| 94. C43 | Dic71 | semidirect |
| 127. C42 | C4⋊Dic71 | semidirect |
| 157. C4 | #17985867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985867 | 2 |
| #22586570 | 2 |
| #22586567 | 2 |
| C2×C43×C71 | 2 |
| #14688 | 71 |