Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
192 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 66 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 | H(3,ℤ/4) |
| commutator | C2×C8 | C42×C71 |
| Frattini, cosocle | C4×M16 | C22×C71 |
| socle | C2×C71 | #1288 |
| prime radical | C23×C71 | #104 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C71 ◁ C2×C8×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #347×C71 | C4 | semidirect |
| 14. #322×C71 | C4 | semidirect |
| 15. C82×C71 | C4 | semidirect |
| 76. #7225 | C71 | direct (N × H) |
| 83. C71 | #7225 | direct (N × H) |
| 88. #347 | C4×C71 | semidirect |
| 94. #322 | C4×C71 | semidirect |
| 95. C82 | C4×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2165 | 2 |
| C71×#1841 | 2 |
| C71×#1455 | 2 |
| #7225 | 71 |