Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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×#20258593 | C2 | semidirect |
| 2. C22×C379⋊C8 | C2 | semidirect |
| 4. #27131262 | C2 | semidirect |
| 5. #27131255 | C2 | semidirect |
| 6. #27131251 | C2 | semidirect |
| 7. C22⋊Q8×C379 | C2 | semidirect |
| 27. C379⋊C8 | D4 | semidirect |
| 39. C22×C379 | SD16 | semidirect |
| 55. C379 | #465 | semidirect |
| 59. C22⋊Q8 | D379 | semidirect |
| 98. C22 | #20258593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258593 | 2 |
| C22×C379⋊C8 | 2 |
| #27131305 | 2 |
| #27131262 | 2 |
| #27131255 | 2 |
| #27131251 | 2 |
| C22⋊Q8×C379 | 2 |
| #465 | 379 |