Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #99 |
| commutator | C22×C4 | C42×C71 |
| Frattini, cosocle | C2×C4×D4 | C22×C71 |
| socle | C22×C71 | #342 |
| prime radical | C22×D4×C71 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C22×C4×C71 ◁ C2×C4×D4×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×M16×C71 | C4 | semidirect |
| 9. C2×C22⋊C8×C71 | C4 | semidirect |
| 12. #343×C71 | C4 | semidirect |
| 137. #7282 | C71 | direct (N × H) |
| 148. C71 | #7282 | direct (N × H) |
| 149. C22×M16 | C4×C71 | semidirect |
| 154. C2×C22⋊C8 | C4×C71 | semidirect |
| 157. #343 | C4×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#1870 | 2 |
| C4×#100×C71 | 2 |
| C4×#99×C71 | 2 |
| #7282 | 71 |