Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #22611704 | C2 | semidirect |
| 5. #22610679 | C2 | semidirect |
| 6. #22608033 | C2 | semidirect |
| 7. C73×#1376 | C2 | semidirect |
| 21. #17988398 | C4 | semidirect |
| 46. #14556523 | C2×C4 | semidirect |
| 57. M32×C73 | C2×C4 | semidirect |
| 161. #1376 | D73 | semidirect |
| 162. C73 | #12951 | semidirect |
| 203. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556613 | 2 |
| #22611704 | 2 |
| #22611681 | 2 |
| #22611668 | 2 |
| #22610679 | 2 |
| #22608033 | 2 |
| C73×#1376 | 2 |
| #12951 | 73 |