Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #22586305 | C2 | semidirect |
| 5. #22586304 | C2 | semidirect |
| 6. #22586303 | C2 | semidirect |
| 7. C71×#1332 | C2 | semidirect |
| 72. Dic284 | M16 | semidirect |
| 95. Q16×C71 | M16 | semidirect |
| 161. #1332 | D71 | semidirect |
| 162. C71 | #11658 | semidirect |
| 231. Q16 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D71 | 2 |
| #22590137 | 2 |
| #22587097 | 2 |
| #22586305 | 2 |
| #22586304 | 2 |
| #22586303 | 2 |
| C71×#1332 | 2 |
| #11658 | 71 |