Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
212 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 212 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, socle | C22×C71 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C71 |
| prime radical | C2×D4×C71 | D8 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C42×C71 ◁ C8×D4×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C71×#2254 | C2 | semidirect |
| 5. C71×#1371 | C2 | semidirect |
| 6. C71×#1365 | C2 | semidirect |
| 7. C71×#1364 | C2 | semidirect |
| 65. C16×C71 | SD16 | semidirect |
| 98. #12456 | C71 | direct (N × H) |
| 103. #2254 | C2×C71 | semidirect |
| 107. #1371 | C2×C71 | semidirect |
| 108. #1365 | C2×C71 | semidirect |
| 109. #1364 | C2×C71 | semidirect |
| 110. C71 | #12456 | direct (N × H) |
| 168. C16 | SD16×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2254 | 2 |
| C71×#2169 | 2 |
| C71×#1675 | 2 |
| C71×#1673 | 2 |
| C71×#1371 | 2 |
| C71×#1365 | 2 |
| C71×#1364 | 2 |
| #12456 | 71 |