Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#17985822 | C2 | semidirect |
| 5. #22589130 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 7. C71×#1378 | C2 | semidirect |
| 21. #17985807 | C4 | semidirect |
| 45. #14556064 | C2×C4 | semidirect |
| 59. C2×C16×C71 | C2×C4 | semidirect |
| 158. #1378 | D71 | semidirect |
| 159. C71 | #12949 | semidirect |
| 202. C2×C16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597225 | 2 |
| C2×#17985822 | 2 |
| #22590090 | 2 |
| #22590069 | 2 |
| #22589130 | 2 |
| #22586439 | 2 |
| C71×#1378 | 2 |
| #12949 | 71 |