Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 114 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. #22626137 | C2 | semidirect |
| 2. C2×#17989448 | C2 | semidirect |
| 3. #22624892 | C2 | semidirect |
| 4. #22624890 | C2 | semidirect |
| 30. #14556613 | C8 | semidirect |
| 71. Dic292 | C2×C8 | semidirect |
| 74. D584 | C2×C8 | semidirect |
| 154. C73 | #11598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626137 | 2 |
| C2×#17989448 | 2 |
| #22624892 | 2 |
| #22624890 | 2 |
| #22618702 | 2 |
| #11598 | 73 |