Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22627147 | C2 | semidirect |
| 2. #22627146 | C2 | semidirect |
| 3. #22626996 | C2 | semidirect |
| 4. #22626974 | C2 | semidirect |
| 5. D4⋊#11924040 | C2 | semidirect |
| 6. C8×#11924040 | C2 | semidirect |
| 49. #11924040 | D8 | semidirect |
| 93. #10596831 | M32 | semidirect |
| 121. C73 | #12039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627147 | 2 |
| #22627146 | 2 |
| #22626996 | 2 |
| #22626974 | 2 |
| D4⋊#11924040 | 2 |
| C8×#11924040 | 2 |
| #22625511 | 2 |
| #12039 | 73 |