Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22598056 | C2 | semidirect |
| 3. #22597989 | C2 | semidirect |
| 4. C2×#17985813 | C2 | semidirect |
| 5. #22589967 | C2 | semidirect |
| 6. #22586456 | C2 | semidirect |
| 7. C71×#2145 | C2 | semidirect |
| 59. #14556068 | D4 | semidirect |
| 62. #14556064 | D4 | semidirect |
| 71. C2×Q16×C71 | D4 | semidirect |
| 73. C2×D8×C71 | D4 | semidirect |
| 216. #2145 | D71 | semidirect |
| 219. C71 | #13310 | semidirect |
| 255. C2×Q16 | D284 | semidirect |
| 263. C2×D8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| #22598056 | 2 |
| #22597989 | 2 |
| C2×#17985813 | 2 |
| #22589967 | 2 |
| #22586456 | 2 |
| C71×#2145 | 2 |
| #13310 | 71 |