Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#21418732 | C2 | semidirect |
| 2. C2×#21418731 | C2 | semidirect |
| 3. C2×#21418728 | C2 | semidirect |
| 4. #28417949 | C2 | semidirect |
| 5. #28417940 | C2 | semidirect |
| 6. #28417863 | C2 | semidirect |
| 7. C2×D8×C467 | C2 | semidirect |
| 29. C467⋊C8 | D4 | semidirect |
| 37. C8×C467 | D4 | semidirect |
| 54. C467 | #496 | semidirect |
| 59. C2×D8 | D467 | semidirect |
| 92. C8 | C22⋊D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21418732 | 2 |
| C2×#21418731 | 2 |
| C2×#21418728 | 2 |
| #28417949 | 2 |
| #28417940 | 2 |
| #28417863 | 2 |
| C2×D8×C467 | 2 |
| #496 | 467 |