Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
662 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 134 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 | C42 | C22×C4×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| prime radical | C2×#496×C71 | C2 |
| LCS | G ▷ 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 |
|---|---|---|
| 2. C71×#2379 | C2 | semidirect |
| 3. C71×#1961 | C2 | semidirect |
| 4. C2×#329×C71 | C2 | semidirect |
| 5. C71×#1295 | C2 | semidirect |
| 11. #496×C71 | C4 | semidirect |
| 37. #127×C71 | C2×C4 | semidirect |
| 54. #97×C71 | C2×C4 | semidirect |
| 171. #9001 | C71 | direct (N × H) |
| 180. #2379 | C2×C71 | semidirect |
| 181. #1961 | C2×C71 | semidirect |
| 182. C2×#329 | C2×C71 | semidirect |
| 183. #1295 | C2×C71 | semidirect |
| 184. C71 | #9001 | direct (N × H) |
| 190. #496 | C4×C71 | semidirect |
| 216. #127 | C2×C4×C71 | semidirect |
| 233. #97 | C2×C4×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#496×C71 | 2 |
| C71×#2379 | 2 |
| C71×#1961 | 2 |
| C2×#329×C71 | 2 |
| C71×#1295 | 2 |
| #9001 | 71 |