Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1074 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22588801 | C2 | semidirect |
| 3. #22588638 | C2 | semidirect |
| 4. #22586701 | C2 | semidirect |
| 5. C71×#1465 | C2 | semidirect |
| 7. C22×#11765849 | C22 | semidirect |
| 19. C2×C22⋊(C71⋊C8) | C22 | semidirect |
| 24. #407×C71 | C22 | semidirect |
| 154. C23×C71 | #100 | semidirect |
| 180. C2×C4×C71 | #100 | semidirect |
| 243. #1465 | D71 | semidirect |
| 244. C71 | #8536 | semidirect |
| 258. #407 | C2×D71 | semidirect |
| 400. C23 | #14556044 | semidirect |
| 434. C2×C4 | #14556044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602104 | 2 |
| #22588801 | 2 |
| #22588638 | 2 |
| #22586701 | 2 |
| C71×#1465 | 2 |
| #8536 | 71 |