Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1280 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1280 conjugacy classes of subgroups — too many to draw. Only its 191 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×#17986603 | C2 | semidirect |
| 2. C2×#17986375 | C2 | semidirect |
| 3. C2×#17986364 | C2 | semidirect |
| 4. #22594093 | C2 | semidirect |
| 5. #22589337 | C2 | semidirect |
| 6. #22589304 | C2 | semidirect |
| 7. #22588686 | C2 | semidirect |
| 8. #22588109 | C2 | semidirect |
| 9. C71×#1961 | C2 | semidirect |
| 48. #14556120 | D4 | semidirect |
| 74. #127×C71 | D4 | semidirect |
| 214. #1961 | D71 | semidirect |
| 217. C71 | #25608 | semidirect |
| 259. #127 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986603 | 2 |
| C2×#17986375 | 2 |
| C2×#17986364 | 2 |
| #22594093 | 2 |
| #22589337 | 2 |
| #22589304 | 2 |
| #22588686 | 2 |
| #22588109 | 2 |
| C71×#1961 | 2 |
| #25608 | 71 |