Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#17986440 | C2 | semidirect |
| 2. C2×#17986271 | C2 | semidirect |
| 4. C2×#17985807 | C2 | semidirect |
| 5. C2×#17985782 | C2 | semidirect |
| 6. #22586448 | C2 | semidirect |
| 7. C2×#358×C71 | C2 | semidirect |
| 60. #14556068 | D4 | semidirect |
| 63. #14556064 | D4 | semidirect |
| 73. C2×Q16×C71 | D4 | semidirect |
| 216. C2×#358 | D71 | semidirect |
| 219. C71 | #13308 | semidirect |
| 259. C2×Q16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986440 | 2 |
| C2×#17986271 | 2 |
| #22598012 | 2 |
| C2×#17985807 | 2 |
| C2×#17985782 | 2 |
| #22586448 | 2 |
| C2×#358×C71 | 2 |
| #13308 | 71 |