Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
434 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C23 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×C4⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3245 | C2 | semidirect |
| 2. C23×#2184 | C2 | semidirect |
| 3. C23×#2054 | C2 | semidirect |
| 4. C23×#1347 | C2 | semidirect |
| 5. C23×#1322 | C2 | semidirect |
| 84. #12158 | C23 | direct (N × H) |
| 116. C2×C4×C23 | D16 | semidirect |
| 121. #3245 | C2×C23 | semidirect |
| 122. #2184 | C2×C23 | semidirect |
| 123. #2054 | C2×C23 | semidirect |
| 124. #1347 | C2×C23 | semidirect |
| 125. #1322 | C2×C23 | semidirect |
| 195. C23 | #12158 | direct (N × H) |
| 265. C2×C4 | C23×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3245 | 2 |
| C23×#2184 | 2 |
| C23×#2054 | 2 |
| C23×#1347 | 2 |
| C23×#1322 | 2 |
| #12158 | 23 |