Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
578 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22599329 | C2 | semidirect |
| 3. #22598808 | C2 | semidirect |
| 4. #22586756 | C2 | semidirect |
| 5. #22586691 | C2 | semidirect |
| 6. #22586211 | C2 | semidirect |
| 7. C71×#1496 | C2 | semidirect |
| 216. #1496 | 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 |
| #22599329 | 2 |
| #22598808 | 2 |
| #22586756 | 2 |
| #22586691 | 2 |
| #22586211 | 2 |
| C71×#1496 | 2 |
| #10120 | 71 |