Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 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. #22612181 | C2 | semidirect |
| 2. #22612180 | C2 | semidirect |
| 3. #22612156 | C2 | semidirect |
| 4. #22609545 | C2 | semidirect |
| 5. #22609524 | C2 | semidirect |
| 6. #22607850 | C2 | semidirect |
| 7. C73×#2240 | C2 | semidirect |
| 97. #10596831 | D16 | semidirect |
| 123. #2240 | D73 | semidirect |
| 127. C73 | #12525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612181 | 2 |
| #22612180 | 2 |
| #22612156 | 2 |
| #22609545 | 2 |
| #22609524 | 2 |
| #22607850 | 2 |
| C73×#2240 | 2 |
| #12525 | 73 |