Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
662 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 662 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. #22620397 | C2 | semidirect |
| 2. #22620022 | C2 | semidirect |
| 3. #22615783 | C2 | semidirect |
| 4. #22608554 | C2 | semidirect |
| 5. #22608479 | C2 | semidirect |
| 6. #22607796 | C2 | semidirect |
| 7. C73×#1490 | C2 | semidirect |
| 44. #14556591 | D4 | semidirect |
| 45. #14556588 | D4 | semidirect |
| 64. #14556502 | D4 | semidirect |
| 83. C4×C8×C73 | D4 | semidirect |
| 233. #1490 | D73 | semidirect |
| 235. C73 | #10018 | semidirect |
| 307. C4×C8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620397 | 2 |
| #22620022 | 2 |
| #22615783 | 2 |
| #22608554 | 2 |
| #22608479 | 2 |
| #22607796 | 2 |
| C73×#1490 | 2 |
| #10018 | 73 |