Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590607 | C2 | semidirect |
| 2. #22590380 | C2 | semidirect |
| 3. #22587819 | C2 | semidirect |
| 4. #22586383 | C2 | semidirect |
| 5. #22586310 | C2 | semidirect |
| 6. #22586298 | C2 | semidirect |
| 7. C71×#3277 | C2 | semidirect |
| 93. Q16×C71 | D8 | semidirect |
| 173. #3277 | D71 | semidirect |
| 180. C71 | #12325 | semidirect |
| 258. Q16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590607 | 2 |
| #22590380 | 2 |
| #22587819 | 2 |
| #22586383 | 2 |
| #22586310 | 2 |
| #22586298 | 2 |
| C71×#3277 | 2 |
| #12325 | 71 |