Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22587254 | C2 | semidirect |
| 2. #22587164 | C2 | semidirect |
| 3. #22586406 | C2 | semidirect |
| 4. #22586307 | C2 | semidirect |
| 5. #22586307 | C2 | semidirect |
| 6. #22586262 | C2 | semidirect |
| 58. D8×C71 | M16 | semidirect |
| 116. C71 | #12078 | semidirect |
| 160. D8 | #11765849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22587254 | 2 |
| #22587164 | 2 |
| #22586406 | 2 |
| #22586307 | 2 |
| #22586262 | 2 |
| C71×#2177 | 2 |
| #12078 | 71 |