Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22599339 | C2 | semidirect |
| 2. #22598716 | C2 | semidirect |
| 4. #22587053 | C2 | semidirect |
| 5. #22586939 | C2 | semidirect |
| 6. #22586233 | C2 | semidirect |
| 7. C71×#1506 | C2 | semidirect |
| 53. C4⋊(C71⋊C8) | D4 | semidirect |
| 60. #14556039 | D4 | semidirect |
| 62. C4⋊Q8×C71 | D4 | semidirect |
| 63. C4⋊Q8×C71 | D4 | semidirect |
| 206. #1506 | D71 | semidirect |
| 208. C71 | #10096 | semidirect |
| 241. C4⋊Q8 | D284 | semidirect |
| 242. C4⋊Q8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599339 | 2 |
| #22598716 | 2 |
| #22594446 | 2 |
| #22587053 | 2 |
| #22586939 | 2 |
| #22586233 | 2 |
| C71×#1506 | 2 |
| #10096 | 71 |