Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22599255 | C2 | semidirect |
| 2. #22597800 | C2 | semidirect |
| 3. #22593282 | C2 | semidirect |
| 4. #22587007 | C2 | semidirect |
| 5. #22586732 | C2 | semidirect |
| 6. #22586243 | C2 | semidirect |
| 7. C71×#1502 | C2 | semidirect |
| 58. C4⋊(C71⋊C8) | D4 | semidirect |
| 59. C4⋊(C71⋊C8) | D4 | semidirect |
| 66. C4⋊Q8×C71 | D4 | semidirect |
| 67. #127×C71 | D4 | semidirect |
| 102. C2×D284 | D8 | semidirect |
| 245. #1502 | D71 | semidirect |
| 248. C71 | #10238 | semidirect |
| 285. C4⋊Q8 | D284 | semidirect |
| 292. #127 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599255 | 2 |
| #22597800 | 2 |
| #22593282 | 2 |
| #22587007 | 2 |
| #22586732 | 2 |
| #22586243 | 2 |
| C71×#1502 | 2 |
| #10238 | 71 |