Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D467 |
| commutator, socle, cosocle | C22×C467 | C24 |
| Fitting | C22⋊Q8×C467 | C2 |
| hypercenter | C22⋊Q8 | D467 |
| hypocenter | C467 | #548 |
| LCS | G ▷ C22×C467 ▷ C467 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#21418743 | C2 | semidirect |
| 2. C2×Q8×D467 | C2 | semidirect |
| 3. #28417942 | C2 | semidirect |
| 4. #28417939 | C2 | semidirect |
| 5. #28417931 | C2 | semidirect |
| 6. #28417928 | C2 | semidirect |
| 7. #28417926 | C2 | semidirect |
| 8. #28417918 | C2 | semidirect |
| 9. #28417915 | C2 | semidirect |
| 10. C4×C22⋊D467 | C2 | semidirect |
| 11. C22⋊Q8×C467 | C2 | semidirect |
| 40. Dic934 | D4 | semidirect |
| 68. C2×D467 | #41 | semidirect |
| 83. C467 | #548 | semidirect |
| 90. C22⋊Q8 | D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21418743 | 2 |
| C2×Q8×D467 | 2 |
| #28417942 | 2 |
| #28417939 | 2 |
| #28417931 | 2 |
| #28417928 | 2 |
| #28417926 | 2 |
| #28417918 | 2 |
| #28417915 | 2 |
| C4×C22⋊D467 | 2 |
| C22⋊Q8×C467 | 2 |
| #548 | 467 |