Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 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×Q8×D379 | C2 | semidirect |
| 2. C2×#20258595 | C2 | semidirect |
| 3. C2×#20258593 | C2 | semidirect |
| 5. #27131254 | C2 | semidirect |
| 6. (C2×D379)⋊C8 | C2 | semidirect |
| 7. #103×C379 | C2 | semidirect |
| 27. Dic758 | D4 | semidirect |
| 38. Q8×C379 | D4 | semidirect |
| 49. C2×D379 | SD16 | semidirect |
| 61. C379 | #448 | semidirect |
| 68. #103 | D379 | semidirect |
| 91. Q8 | D1516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D379 | 2 |
| C2×#20258595 | 2 |
| C2×#20258593 | 2 |
| #27131306 | 2 |
| #27131254 | 2 |
| (C2×D379)⋊C8 | 2 |
| #103×C379 | 2 |
| #448 | 379 |