Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | #1533 |
| commutator | C42 | C22×C4×C71 |
| Frattini, cosocle | #97 | C23×C71 |
| prime radical | C2×#127×C71 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C2×C4×C71 ◁ C4×M16×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C71×#2165 | C2 | semidirect |
| 3. C71×#1355 | C2 | semidirect |
| 13. #347×C71 | C22 | semidirect |
| 83. #11915 | C71 | direct (N × H) |
| 89. #2165 | C2×C71 | semidirect |
| 90. #1355 | C2×C71 | semidirect |
| 91. C71 | #11915 | direct (N × H) |
| 101. #347 | C22×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#3138 | 2 |
| C71×#2165 | 2 |
| C71×#1355 | 2 |
| #11915 | 71 |