Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #22597363 | C2 | semidirect |
| 3. #22588329 | C2 | semidirect |
| 4. #22587009 | C2 | semidirect |
| 5. #22587007 | C2 | semidirect |
| 6. #22586243 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 50. C4⋊(C71⋊C8) | D4 | semidirect |
| 61. C4⋊C8×C71 | D4 | semidirect |
| 203. #1303 | D71 | semidirect |
| 204. C71 | #9397 | semidirect |
| 254. C4⋊C8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597363 | 2 |
| #22593282 | 2 |
| #22588329 | 2 |
| #22587009 | 2 |
| #22587007 | 2 |
| #22586243 | 2 |
| C71×#1303 | 2 |
| #9397 | 71 |