Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22623065 | C2 | semidirect |
| 2. #22619512 | C2 | semidirect |
| 3. #22611667 | C2 | semidirect |
| 4. #22611666 | C2 | semidirect |
| 5. #22611542 | C2 | semidirect |
| 6. #22608032 | C2 | semidirect |
| 7. C73×#3050 | C2 | semidirect |
| 38. C2×Dic292 | D4 | semidirect |
| 40. C2×D584 | D4 | semidirect |
| 56. C2×#11924003 | D4 | semidirect |
| 58. #14556523 | D4 | semidirect |
| 67. C2×Q16×C73 | D4 | semidirect |
| 69. C2×D8×C73 | D4 | semidirect |
| 85. #106×C73 | D4 | semidirect |
| 235. #3050 | D73 | semidirect |
| 240. C73 | #13309 | semidirect |
| 278. C2×Q16 | C22⋊D73 | semidirect |
| 282. C2×D8 | C22⋊D73 | semidirect |
| 316. #106 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623065 | 2 |
| #22619512 | 2 |
| #22611667 | 2 |
| #22611666 | 2 |
| #22611542 | 2 |
| #22608032 | 2 |
| C73×#3050 | 2 |
| #13309 | 73 |