Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
604 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 604 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. C2×#17986435 | C2 | semidirect |
| 2. #22597949 | C2 | semidirect |
| 3. C2×#17985808 | C2 | semidirect |
| 4. #22590056 | C2 | semidirect |
| 5. C2×#17985781 | C2 | semidirect |
| 6. #22586447 | C2 | semidirect |
| 7. C2×#469×C71 | C2 | semidirect |
| 36. C2×Dic284 | D4 | semidirect |
| 38. C2×D568 | D4 | semidirect |
| 50. #14556068 | D4 | semidirect |
| 53. #14556062 | D4 | semidirect |
| 65. C2×D8×C71 | D4 | semidirect |
| 79. #106×C71 | D4 | semidirect |
| 223. C2×#469 | D71 | semidirect |
| 228. C71 | #13316 | semidirect |
| 268. C2×D8 | C22⋊D71 | semidirect |
| 298. #106 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986435 | 2 |
| #22597949 | 2 |
| C2×#17985808 | 2 |
| #22590056 | 2 |
| C2×#17985781 | 2 |
| #22586447 | 2 |
| C2×#469×C71 | 2 |
| #13316 | 71 |