Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
364 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 364 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 | C22×C71 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C71 |
| prime radical | #532×C71 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C71×#1849 | C2 | semidirect |
| 3. C71×#1559 | C2 | semidirect |
| 5. C71×#1531 | C2 | semidirect |
| 7. C71×#1307 | C2 | semidirect |
| 149. #10526 | C71 | direct (N × H) |
| 156. #1849 | C2×C71 | semidirect |
| 157. #1559 | C2×C71 | semidirect |
| 159. #1531 | C2×C71 | semidirect |
| 161. #1307 | C2×C71 | semidirect |
| 162. C71 | #10526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#3254 | 2 |
| C71×#1849 | 2 |
| C71×#1559 | 2 |
| C71×#1557 | 2 |
| C71×#1531 | 2 |
| C71×#1530 | 2 |
| C71×#1307 | 2 |
| #10526 | 71 |