Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
400 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C71 | #331 |
| commutator | C42 | C22×C4×C71 |
| Frattini, cosocle | C4×C8 | C23×C71 |
| socle | C2×C71 | C2×#331 |
| prime radical | C71×#3147 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C71 ◁ C22×C4×C71 ◁ C2×C4×C8×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#364×C71 | C2 | semidirect |
| 3. C71×#1359 | C2 | semidirect |
| 93. #11922 | C71 | direct (N × H) |
| 99. C2×#364 | C2×C71 | semidirect |
| 100. #1359 | C2×C71 | semidirect |
| 101. C71 | #11922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#3147 | 2 |
| C2×#364×C71 | 2 |
| C71×#1359 | 2 |
| #11922 | 71 |