Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
712 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C71 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C71 |
| prime radical | C71×#2537 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ C2×C42×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#476×C71 | C2 | semidirect |
| 3. C71×#1956 | C2 | semidirect |
| 4. C2×D4⋊C8×C71 | C2 | semidirect |
| 5. C71×#1296 | C2 | semidirect |
| 28. C4⋊Q8×C71 | D4 | semidirect |
| 44. C4⋊C8×C71 | D4 | semidirect |
| 152. #10235 | C71 | direct (N × H) |
| 159. C2×#476 | C2×C71 | semidirect |
| 161. #1956 | C2×C71 | semidirect |
| 162. C2×D4⋊C8 | C2×C71 | semidirect |
| 163. #1296 | C2×C71 | semidirect |
| 164. C71 | #10235 | direct (N × H) |
| 187. C4⋊Q8 | D4×C71 | semidirect |
| 203. C4⋊C8 | D4×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#476×C71 | 2 |
| C71×#2537 | 2 |
| C71×#1956 | 2 |
| C2×D4⋊C8×C71 | 2 |
| C71×#1296 | 2 |
| #10235 | 71 |