Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
676 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 676 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 | C2×#127×C71 | C22 |
| 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 |
|---|---|---|
| 2. C71×#2582 | C2 | semidirect |
| 4. C2×Q8⋊C8×C71 | C2 | semidirect |
| 5. C71×#1296 | C2 | semidirect |
| 55. C2×Q8×C71 | SD16 | semidirect |
| 146. #10230 | C71 | direct (N × H) |
| 154. #2582 | C2×C71 | semidirect |
| 156. C2×Q8⋊C8 | C2×C71 | semidirect |
| 157. #1296 | C2×C71 | semidirect |
| 158. C71 | #10230 | direct (N × H) |
| 208. C2×Q8 | SD16×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#460×C71 | 2 |
| C71×#2582 | 2 |
| C71×#1957 | 2 |
| C2×Q8⋊C8×C71 | 2 |
| C71×#1296 | 2 |
| #10230 | 71 |