Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22590137 | C2 | semidirect |
| 3. #22587097 | C2 | semidirect |
| 4. #22586304 | C2 | semidirect |
| 5. #22586302 | C2 | semidirect |
| 6. #22586300 | C2 | semidirect |
| 7. C71×#1332 | C2 | semidirect |
| 74. D568 | M16 | semidirect |
| 95. Q16×C71 | M16 | semidirect |
| 164. #1332 | D71 | semidirect |
| 167. C71 | #11660 | semidirect |
| 234. Q16 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556151 | 2 |
| #22590137 | 2 |
| #22587097 | 2 |
| #22586304 | 2 |
| #22586302 | 2 |
| #22586300 | 2 |
| C71×#1332 | 2 |
| #11660 | 71 |