Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
140 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | #1347 |
| commutator | C2×C16 | C2×C4×C71 |
| Frattini, cosocle | C2×M32 | C22×C71 |
| prime radical | C23×C71 | D16 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C2×C4×C71 ◁ C22×C8×C71 ◁ C2×M32×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×Q32×C71 | C4 | semidirect |
| 9. #367×C71 | C4 | semidirect |
| 62. #7423 | C71 | direct (N × H) |
| 69. C71 | #7423 | direct (N × H) |
| 70. C2×Q32 | C4×C71 | semidirect |
| 75. #367 | C4×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2219 | 2 |
| C71×#1400 | 2 |
| C71×#1384 | 2 |
| #7423 | 71 |