Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
604 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 604 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×#17986434 | C2 | semidirect |
| 2. #22597945 | C2 | semidirect |
| 3. C2×#17986253 | C2 | semidirect |
| 4. #22590057 | C2 | semidirect |
| 5. C2×#17985780 | C2 | semidirect |
| 6. #22586447 | C2 | semidirect |
| 7. C2×#360×C71 | C2 | semidirect |
| 39. C2×D568 | D4 | semidirect |
| 59. #14556068 | D4 | semidirect |
| 61. #14556062 | D4 | semidirect |
| 71. C2×Q16×C71 | D4 | semidirect |
| 73. C2×D8×C71 | D4 | semidirect |
| 80. #106×C71 | D4 | semidirect |
| 224. C2×#360 | D71 | semidirect |
| 228. C71 | #13316 | semidirect |
| 260. C2×Q16 | D284 | semidirect |
| 268. C2×D8 | D284 | 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×#17986434 | 2 |
| #22597945 | 2 |
| C2×#17986253 | 2 |
| #22590057 | 2 |
| C2×#17985780 | 2 |
| #22586447 | 2 |
| C2×#360×C71 | 2 |
| #13316 | 71 |