Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#17986120 | C2 | semidirect |
| 3. C2×#17985811 | C2 | semidirect |
| 4. C2×#17985808 | C2 | semidirect |
| 5. #22589214 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 7. C71×#1383 | C2 | semidirect |
| 13. C2×#14556073 | C4 | semidirect |
| 14. C2×D1136 | C4 | semidirect |
| 85. Dic284 | C22⋊C4 | semidirect |
| 93. D568 | C22⋊C4 | semidirect |
| 183. #1383 | D71 | semidirect |
| 185. C71 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986437 | 2 |
| C2×#17986120 | 2 |
| C2×#17985811 | 2 |
| C2×#17985808 | 2 |
| #22589214 | 2 |
| #22586419 | 2 |
| C71×#1383 | 2 |
| #13040 | 71 |