Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22586311 | C2 | semidirect |
| 5. #22586310 | C2 | semidirect |
| 6. #22586309 | C2 | semidirect |
| 7. C71×#1334 | C2 | semidirect |
| 72. Dic284 | M16 | semidirect |
| 95. Q16×C71 | M16 | semidirect |
| 159. #1334 | D71 | semidirect |
| 160. C71 | #11664 | semidirect |
| 229. 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 |
| #22590141 | 2 |
| #22587094 | 2 |
| #22586311 | 2 |
| #22586310 | 2 |
| #22586309 | 2 |
| C71×#1334 | 2 |
| #11664 | 71 |