Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22599331 | C2 | semidirect |
| 2. #22599327 | C2 | semidirect |
| 3. #22586809 | C2 | semidirect |
| 4. #22586758 | C2 | semidirect |
| 5. #22586692 | C2 | semidirect |
| 6. #22586212 | C2 | semidirect |
| 7. C71×#3153 | C2 | semidirect |
| 215. #3153 | D71 | semidirect |
| 220. C71 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599331 | 2 |
| #22599327 | 2 |
| #22586809 | 2 |
| #22586758 | 2 |
| #22586692 | 2 |
| #22586212 | 2 |
| C71×#3153 | 2 |
| #10120 | 71 |