Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
562 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C71 |
| prime radical | C71×#3192 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#481×C71 | C2 | semidirect |
| 3. C2×#480×C71 | C2 | semidirect |
| 4. C71×#1821 | C2 | semidirect |
| 5. C71×#1471 | C2 | semidirect |
| 6. C71×#1471 | C2 | semidirect |
| 7. C71×#1298 | C2 | semidirect |
| 194. #9992 | C71 | direct (N × H) |
| 204. C2×#481 | C2×C71 | semidirect |
| 205. C2×#480 | C2×C71 | semidirect |
| 206. #1821 | C2×C71 | semidirect |
| 207. #1471 | C2×C71 | semidirect |
| 208. #1471 | C2×C71 | semidirect |
| 209. #1298 | C2×C71 | semidirect |
| 210. C71 | #9992 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#3192 | 2 |
| C2×#481×C71 | 2 |
| C2×#480×C71 | 2 |
| C71×#1821 | 2 |
| C71×#1471 | 2 |
| C71×#1298 | 2 |
| #9992 | 71 |