Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
608 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C23 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C4×Q8×C23 ◁ C8×Q8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3391 | C2 | semidirect |
| 2. C23×#2246 | C2 | semidirect |
| 3. C23×#2206 | C2 | semidirect |
| 4. Q8×C16×C23 | C2 | semidirect |
| 5. C4×C23×D16 | C2 | semidirect |
| 48. C16×C23 | #41 | semidirect |
| 49. #33958 | C23 | direct (N × H) |
| 51. Q8×C23 | D16 | semidirect |
| 64. #3391 | C2×C23 | semidirect |
| 65. #2246 | C2×C23 | semidirect |
| 66. #2206 | C2×C23 | semidirect |
| 67. Q8×C16 | C2×C23 | semidirect |
| 68. C4×D16 | C2×C23 | semidirect |
| 108. C23 | #33958 | direct (N × H) |
| 125. C16 | #41×C23 | semidirect |
| 127. Q8 | C23×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3391 | 2 |
| C23×#2246 | 2 |
| C23×#2206 | 2 |
| Q8×C16×C23 | 2 |
| C4×C23×D16 | 2 |
| #33958 | 23 |