Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
576 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 576 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. #22620318 | C2 | semidirect |
| 2. #22620030 | C2 | semidirect |
| 4. #22608554 | C2 | semidirect |
| 5. #22608483 | C2 | semidirect |
| 6. #22607796 | C2 | semidirect |
| 7. C73×#1490 | C2 | semidirect |
| 37. #14556591 | D4 | semidirect |
| 38. #14556591 | D4 | semidirect |
| 62. #14556502 | D4 | semidirect |
| 81. C4×C8×C73 | D4 | semidirect |
| 216. #1490 | D73 | semidirect |
| 218. C73 | #10022 | semidirect |
| 288. C4×C8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620318 | 2 |
| #22620030 | 2 |
| #22615783 | 2 |
| #22608554 | 2 |
| #22608483 | 2 |
| #22607796 | 2 |
| C73×#1490 | 2 |
| #10022 | 73 |