Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1770 conjugacy classes of subgroups; only the 542 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 542 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C71 | C24 |
| commutator | C23 | C23×C4×C71 |
| Frattini, cosocle | C24 | C24×C71 |
| prime radical | C25×C71 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#383×C71 | C2 | semidirect |
| 3. C2×C43×C71 | C2 | semidirect |
| 5. C71×#1436 | C2 | semidirect |
| 8. C2×#126×C71 | C4 | semidirect |
| 61. C42×C71 | C22⋊C4 | semidirect |
| 85. C2×C4×C71 | #126 | semidirect |
| 100. #14711 | C71 | direct (N × H) |
| 107. C2×#383 | C2×C71 | semidirect |
| 108. C2×C43 | C2×C71 | semidirect |
| 110. #1436 | C2×C71 | semidirect |
| 111. C71 | #14711 | direct (N × H) |
| 114. C2×#126 | C4×C71 | semidirect |
| 167. C42 | C22⋊C4×C71 | semidirect |
| 191. C2×C4 | #126×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#126×C71 | 2 |
| C2×#383×C71 | 2 |
| C2×C43×C71 | 2 |
| C71×#1437 | 2 |
| C71×#1436 | 2 |
| #14711 | 71 |