Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | #117 |
| commutator | C2×C4 | C22×C8×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| socle | C22×C71 | #383 |
| prime radical | C23×C71 | #117 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C2×#97×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 26. #97×C71 | C8 | semidirect |
| 83. #8801 | C71 | direct (N × H) |
| 92. C71 | #8801 | direct (N × H) |
| 114. #97 | C8×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#97×C71 | 2 |
| C71×#1281 | 2 |
| C71×#1276 | 2 |
| C71×#1275 | 2 |
| #8801 | 71 |